{"id":"3c43c78d-200b-45e7-aac5-740de0bfb313","arxiv_id":"2501.18068","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"high","formal_verification":"none","parameter_count":6,"one_line_summary":"The light cone is governed by conformal symmetry, light-front and instant-time quantization are equivalent, and masses can arise dynamically at a renormalization group fixed point.","lead":"Physicists use different ways of doing quantum calculations, one on ordinary time slices and one on the light cone; this paper argues they are secretly the same theory. It also claims particle masses can emerge from a special kind of scale-symmetric interaction, which would help explain why gravity and the universe's expansion look the way they do.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The finite mass-generation results rest on an unproven QED fixed point with anomalous dimension gamma_theta=-1; if that fixed point does not exist, Eqs. (75), (78), and (86) lose their cutoff independence and the cosmological-constant claim collapses.","rationale":"The reader's conditional verdict is appropriate, and the identified weakest assumption is the same one I would single out: existence of the gamma_theta=-1 fixed point. The paper's most striking physical claims--finite vacuum energy, calculable dynamically generated Higgs mass, and a controlled cosmological constant--are encoded in Eqs. (75)-(88), and every one of those equations uses gamma_theta=-1 to remove the cutoff. Section 23 derives gamma_theta=-1 as a self-consistency condition from an assumed Wilson expansion, but it does not prove that four-dimensional QED actually possesses such a fixed point; the paper cites the Johnson-Baker-Willey program but presents no independent nonperturbative evidence. This is a correctness risk, not an internal contradiction: the NJL summation, Ward-identity check, and gap-equation logic are coherent once the fixed point is granted. There is a secondary proof gap in Section 17: Eq. (36) conjugates phi(0) by the same U that shifts phi(x), while U phi(0)U^{-1}=phi(x3,0,0,x0); the displayed equality needs an additional translation-invariance argument. That gap affects the presentation of the light-front/instant-time equivalence but does not change the main assessment, since the equivalence is supported by prior detailed work [15,20]. Overall, the conditional verdict stands unchanged.","tokens_in":21178,"tokens_out":12296,"duration_ms":138803,"concrete_test":"Run noncompact lattice QED with one staggered fermion near the strong-coupling chiral transition and extract the mass anomalous dimension gamma_m from the scaling of the chiral condensate (or from the fermion propagator) at the would-be continuum limit. If the transition is first order, or if gamma_m is not -1 at the critical point, the assumed gamma_theta=-1 fixed point does not exist and the finiteness of Eqs. (78) and (86) is not realized. As a complementary analytic check, solve the Schwinger-Dyson equation for S^{-1}(p) with the full vertex and verify that a consistent solution with gamma_theta=-1 actually exists.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing assumption is the existence of a nontrivial renormalization-group fixed point in four-dimensional QED with anomalous dimension gamma_theta(alpha)=-1. Section 23, Eqs. (70)-(73), does not prove existence: it starts from an assumed fixed-point propagator S^{-1}(p)=/p-m(-p^2/mu^2)^{gamma_theta/2}, assumes a Wilson expansion coefficient (mu^2 x^2)^{gamma_theta/2}, and then derives gamma_theta=-1 by demanding compatibility between the two. That is a self-consistency condition, not an existence proof. The paper inherits the Johnson-Baker-Willey program [25-27], whose status is unresolved. The decisive finite results--the cutoff-free gap equation (75), the finite vacuum energy (78), and the finite Higgs pole (86)--all depend on the cutoff being removable at this fixed point. If no such fixed point exists, or if the anomalous dimension takes a different value there, the logarithms in Lambda survive, the NJL cutoff cannot be eliminated, and the claimed control of the cosmological constant collapses. I regard this as a correctness risk rather than an internal inconsistency, but it is the least secure link in the central argument.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript argues that light-front quantization is not an independent formalism but coincides with instant-time quantization: restricting the unequal-time commutators and anticommutators of free-field theories to equal light-front time reproduces the equal-x+ commutators (Sections 14-15), and a formal unitary conjugation with the operator U of Eq. (34) is claimed to extend the equivalence to interacting theories to all orders (Section 17). The second half develops a dynamical mass-generation scenario: the NJL model dressed by QED at a putative renormalization-group fixed point with anomalous dimension gamma_theta = -1 yields a cutoff-free gap equation (75), a finite vacuum energy (78), and finite Goldstone and Higgs poles (85)-(88); combined with conformal gravity this is claimed to solve the cosmological constant problem and to fit the supernova Hubble data with deceleration parameter q0 = -0.37 (Section 30). The paper also discusses the conformal symmetry of the light cone, the infinite-momentum-frame connection, vacuum-graph structure, light-front AdS/CFT, and the light-front axial Ward identity.","tokens_in":21491,"tokens_out":21182,"duration_ms":223064,"significance":"The stakes are high: if the two central claims held — exact unitary equivalence of instant-time and light-front quantization for interacting theories, and the existence of a 4D QED fixed point with gamma_theta = -1 rendering the dressed NJL model finite — the light-front approach would receive a first-principles justification, and the dynamical Higgs mass, its width, and the vacuum energy would become calculable rather than input. The manuscript deserves credit for explicitness: the commutator algebra of Sections 14-15 is direct and checkable; the NJL gap, vacuum-energy, and bound-state computations of Sections 19-29 give explicit propagators, vertices, and residues; and the Higgs width in Eq. (86) is a concrete in-principle falsifiable prediction that distinguishes a dynamical from an elementary Higgs. The significance is nonetheless conditional: the finite results (75), (78), and (86) inherit their cutoff independence entirely from the unproven gamma_theta = -1 fixed point, and the purported predictions fix only dimensionless ratios, with the overall mass scale M remaining a free input.","major_comments":[{"comment":"The finiteness results at the center of the paper — the cutoff-free gap equation (75), the finite vacuum energy (78), and the finite Higgs pole (86) — all rest on the assumption that four-dimensional QED possesses a nontrivial renormalization-group fixed point with anomalous dimension gamma_theta(alpha) = -1. Section 23 does not establish the existence of such a fixed point: Eq. (70) assumes the fixed-point form of the inverse propagator, Eq. (71) assumes the Wilson-expansion coefficient, and the value gamma_theta = -1 is then obtained as the compatibility condition between the assumed propagator and the matrix element (72), with the step from (71) to (72) itself asserted rather than derived. The fixed point is inherited from the Johnson-Baker-Willey program [25-27], whose status is unresolved; if no such fixed point exists, or if the anomalous dimension takes a different value there, the logarithmic cutoff dependence survives, the cutoff in (75)-(76) cannot be eliminated, and the claims that the vacuum energy and Higgs pole are finite would no longer follow. This is a correctness risk rather than an internal inconsistency, but it is the least secure link in the central argument and should be presented explicitly as an assumption whose failure would invalidate the main results.","section":"Section 23, Eqs. (70)-(73)"},{"comment":"The extension of the instant-time/light-front equivalence to interacting theories 'to all orders in perturbation theory' is a formal conjugation argument, not a derivation. Eq. (34) defines U as a product of translations, and Eq. (36) then inserts U-dagger U = 1 to equate matrix elements; this assumes that U exists as a unitary operator on the interacting Hilbert space, that the light-front vacuum is exactly U|Omega_I>, and that the two quantizations share the same state space. The free-field results of Sections 14-15 do not imply this, and Section 10 itself emphasizes that light-front vacuum graphs require zero-mode and circle-at-infinity treatments, so the vacuum sector is precisely where the equivalence is nontrivial. The framing in Section 16 is also incorrect as stated: the transformation x+ = x0 + x3 and x- = x0 - x3 is a linear coordinate transformation, not a translation, so the sentence 'the transformation x+/- = x0 +/- x3 is not a Lorentz transformation but a translation' should be corrected, and the relation between coordinate redefinitions and the unitary U needs to be articulated. The equivalence for interacting theories may well be true, but as written it is an assumption; the manuscript should separate the rigorous free-field statement (Sections 14-15) from the conjectural interacting extension.","section":"Section 17, Eqs. (34)-(38)"},{"comment":"The paper presents the Higgs pole and the cosmological fit as accomplished calculations, but both contain free parameters that the text does not acknowledge. In Eq. (86), q^2(Higgs) = (2.189 - 0.051i)M mu, where M is the dynamical fermion mass determined by the free inputs g, Lambda, and mu through Eq. (76), and mu is the renormalization subtraction point; the reduction (87) sets mu = M by hand, so the result fixes the dimensionless ratio q^2/M^2 but not the Higgs mass in physical units. Similarly, the supernova fit of Section 30 takes q0 = -0.37 as a fitted parameter in the luminosity-distance formula (89), and the assertion of fit quality 'comparable to that of the standard model dark matter dark energy fit' rests on Fig. 9, which shows neither the data of [33,34] nor any goodness-of-fit statistic. The claims that the Higgs mass is 'calculable' and that conformal gravity fits the accelerating-universe data should be restated as the determination of parameter-free dimensionless ratios and as a fit with a fitted parameter, respectively.","section":"Sections 29-30, Eqs. (86)-(89)"},{"comment":"The claim that the cosmological constant problem is 'completely solved' (end of Section 25 and again in Section 29) is not supported by the derivations in this manuscript. The finite vacuum energy (78) is of order mu^2 M^2 with mu and M free inputs, and no step connects its magnitude to the observed dark-energy scale or to the conformal-gravity cosmology of Eq. (89). The cancellation of the quartic divergence by conformal gravity is asserted (Sections 20 and 29) with a citation to [3], but the manuscript does not demonstrate that the Weyl-squared action (11) is renormalizable with the required counterterm, nor that the sign and coefficient of the graviton-loop contribution match the half-integer fermion-loop quartic divergence. As it stands, 'the vacuum energy is finite and the cosmological constant is under control' is a research program, not a result established in this paper, and the reader cannot verify the load-bearing steps without consulting [3].","section":"Sections 20, 25, and 29"},{"comment":"There is a dimensional tension in the treatment of the four-fermion coupling. Section 23 states that gamma_theta = -1 reduces the dimension of psi-bar-psi from three to two and of (psi-bar-psi)^2 from six to four, so that the four-fermion interaction 'becomes renormalizable to all orders in g,' which would make g dimensionless. But the gap equation (75), written as <Omega_m|psi-bar-psi|Omega_m> = -m mu^2/(4 pi^2) ln(Lambda^2/m mu) = m/g, and its solution (76), M = (Lambda^2/mu) exp(4 pi^2/(mu^2 g)), are dimensionally consistent only if g carries mass dimension -2: then m/g has dimension three, matching the dimension of the left-hand side, and mu^2 g is dimensionless. The manuscript should specify the mass dimension of g at the fixed point and reconcile the renormalizability claim with the explicit powers of mu^2 and Lambda^2 in (75)-(76).","section":"Section 23, Eqs. (75)-(76)"}],"minor_comments":[{"comment":"The sentence 'we turn now to a four-fermion model to see how to see how things work in that particular case' contains a duplicated phrase ('to see how to see how') that should be corrected.","section":"Section 18"},{"comment":"The passage from the unequal-time commutator (26) to the equal-x+ commutator (28) restricts the delta-function delta[(x+ - y+)(x- - y-) - (x_perp - y_perp)^2] to x+ = y+, which is a formal manipulation of a distribution whose argument vanishes quadratically; since this step supports the central equivalence claim of Section 14, a distributional derivation (for instance, integrated against test functions in x-) would put the argument on firmer ground.","section":"Section 14, Eqs. (26)-(28)"},{"comment":"Several nonstandard claims — the gauging of the full chiral SU(2)_L x SU(2)_R x U(1) as 'Quantum Flavordynamics,' the spontaneous breaking of parity, and the conclusion that conformal gravity solves the dark matter, dark energy, and quantum gravity problems — are stated as consequences without derivation in this section; they should be presented as a programmatic outlook or backed by the cited literature.","section":"Section 6"},{"comment":"Fig. 9 shows only the model curves; adding the actual data points with error bars from [33,34] and reporting a goodness-of-fit statistic would substantiate the claimed comparison with the Lambda-CDM fit.","section":"Section 30, Fig. 9"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is heavily self-referential: roughly ten of the thirty-four references are to the author's own prior work, and several load-bearing results are cited rather than derived in this paper — the interacting-theory equivalence ([15,16,20]), the gamma_theta = -1 mechanism ([28,29]), the dressed-vertex NJL calculations ([30,31]), and the conformal-gravity solution of the cosmological constant problem ([3]). A referee verifying the present manuscript must in effect audit those papers as well; for a journal that treats this manuscript as a synthesis, that is acceptable, but the editor should be aware that the novel technical content largely consists of compilations of earlier results framed by a strong interpretive claim. The paper also spans a very wide range of topics and levels of rigor, from pedagogical review (Sections 1-17) to condensed quotes of earlier derivations (Sections 23-29); a major revision that marks the assumed versus derived status of each central claim would substantially improve verifiability and would make the conditional character of the cosmological-constant and mass-generation claims transparent."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nYou should know this paper is not really a new result: it is a compilation of Mannheim's prior program. The equality of instant-time and light-front quantization, the nonzero light-front vacuum tadpole from circle-at-infinity contributions, the gamma=-1 dynamical mass generation, and the conformal gravity cosmology all appear in his earlier papers. What is new here is mostly packaging, plus a few explicit demonstrations such as the light-front axial-vector Ward identity in Section 31 and the finite NJL calculations in Sections 23-29.\n\nWhat the paper does well: it lays out the equivalence argument cleanly. Starting from unequal-time commutators and deriving the equal light-front-time commutators as a special case is a simple and elegant way to see why the two quantizations agree for free fields. The treatment of vacuum graphs and the role of the circle at infinity is careful, and the NJL gap and vacuum energy calculations under the assumed fixed point are internally consistent. If you want a single reference that states the whole Mannheim program in one place, this is it.\n\nThe soft spots are real and load-bearing. The biggest is the QED fixed point with gamma_theta = -1. The paper does not prove such a fixed point exists. It assumes a fixed-point propagator and Wilson expansion, then derives gamma=-1 as a compatibility condition. That is a self-consistency argument, not an existence proof. If the fixed point does not exist, the cutoff cannot be eliminated in Eqs. (75), (78), and (86), and the claimed finiteness and the cosmological constant solution collapse. The paper inherits the Johnson-Baker-Willey program, whose status has been unresolved for decades. A second fragile point is the unitary operator U in Eq. (34), taken to establish equivalence for interacting theories to all orders. That is asserted, not demonstrated.\n\nI also share the circularity concern. Several \"predictions\" are expressed in terms of free inputs: the Higgs pole position in Section 29 is a function of M and mu and the assumed gamma=-1. The supernova fit in Section 30 uses q0=-0.37 as a fitted parameter, with no error analysis. The claim to solve dark matter, dark energy, and quantum gravity is deferred entirely to prior publication [3]. So the paper is not self-contained evidence for its grandest claims.\n\nWho is this for? A reader who wants a brisk tour of Mannheim's alternative program, or someone working on light-front quantization who wants to see the equivalence argument pushed to its limits. It deserves a serious referee, because the central questions are important and the technical content is substantial, but the referee should be ready to demand evidence for the fixed point.\n\nMy recommendation: send it to peer review, with a referee who knows the JBW literature and will insist on separating the derived results from the assumed ones.","headline":"A sweeping, internally consistent synthesis of Mannheim's program, but the load-bearing QED fixed point is assumed rather than proven, so the grand conclusions rest on a shaky keystone.","tokens_in":22039,"tokens_out":2071,"would_cite":false,"duration_ms":21474,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81T17","81T40"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that light-front quantization is the same theory as instant-time quantization, and that mass scales can be generated dynamically at a fixed point, yielding a finite vacuum energy and a finite Higgs mass.","keywords":["light-front quantization","instant-time quantization","conformal symmetry","dynamical symmetry breaking","anomalous dimension","vacuum energy","cosmological constant","renormalization group fixed point"],"falsifier":"One could settle the mass-generation claim by computing the quantum electromagnetic beta function nonperturbatively (for example, on a spacetime lattice with many fermion flavors) and checking for a fixed point with exponent $-1$. The surface-equivalence claim could be settled by discretizing the same interacting theory on equal-time and null-plane surfaces and comparing the full spectra and matrix elements; any mismatch would disprove the unitary equivalence.","tokens_in":20916,"feed_emoji":"⚛️","tokens_out":11514,"duration_ms":122514,"temperature":0.7,"pith_summary":"This paper argues that light-front quantization is not a separate quantization scheme. Its full symmetry is conformal symmetry, not just Lorentz symmetry, and the apparently different equal-time and equal-light-front-time commutation relations are both slices of one and the same unequal-time commutator; a unitary transformation generated by the momentum operators maps one formalism onto the other to all orders. The paper further argues that the mass scales that take particles off the light cone need not be inserted by hand: a four-fermion interaction dressed by QED at a renormalization-group fixed point spontaneously breaks chiral symmetry, and at the fixed-point value of the anomalous dimension the vacuum energy and the dynamically generated Higgs mass become finite. If both claims hold, the cosmological constant problem loses its fine-tuning and the Higgs boson carries a width that distinguishes a dynamical composite from an elementary scalar.","feed_headline":"Light-front quantization is just instant-time quantization","feed_subtitle":"A unitary change of variables unifies the two formalisms; fixed-point dynamics makes mass and vacuum energy finite","key_machinery":"The machinery has three parts. First, unequal-time commutators: the instant-time commutator $i\\Delta(x-y)$ is a Lorentz-invariant function of $(x-y)^2$, and substituting $x^0=(x^++x^-)/2$, $x^3=(x^+-x^-)/2$ and setting $x^+=y^+$ turns it into the equal-light-front-time commutator. Second, a unitary translation operator $U=\\exp(ix^3\\hat P_0)\\exp(ix^0\\hat P_3)$; since translations are a symmetry of any Poincare-invariant theory, $U$ carries instant-time fields to light-front fields and carries instant-time commutator matrix elements into light-front ones to all orders. Third, a critical fixed point: the dressed fermion propagator $S^{-1}(p)=\\gamma^\\mu p_\\mu - m((-p^2-i\\epsilon)/\\mu^2)^{\\gamma_\\theta(\\alpha)/2}$ at a zero of the QED $\\beta$ function, together with a Wilson expansion for the time-ordered product, is compatible only if $\\gamma_\\theta(\\alpha)=-1$, lowering the dimension of $\\bar\\psi\\psi$ from 3 to 2 and making the four-fermion interaction renormalizable. The $\\gamma_\\theta=-1$ condition is what converts the cut-off-dependent gap equation, vacuum energy, and Higgs residues of the four-fermion model into finite quantities.","core_discovery":"The central assertion is that light-front quantization is instant-time quantization and does not need to be independently postulated. The proof begins from unequal-time commutators: the instant-time commutator $i\\Delta(x-y)$ of a free massless scalar, evaluated at $x^+=y^+$, reproduces the equal-light-front-time commutator with its $\\epsilon(x^-)$ structure, and the same holds for gauge fields and fermion anticommutators. For interacting theories, the paper invokes the unitary operator $U=\\exp(ix^3\\hat P_0)\\exp(ix^0\\hat P_3)$ to transform instant-time fields into light-front fields, so matrix elements of the two commutators agree to all orders. On the mass-generation side, the paper claims that at a QED fixed point with anomalous dimension $\\gamma_\\theta(\\alpha)=-1$, the massless four-fermion theory has an unstable symmetric vacuum; the broken vacuum yields a finite dynamical fermion mass, a finite double-well vacuum energy, a massless Goldstone boson, and a massive Higgs boson with $q^2=(2.189-0.051i)M\\mu$ and a calculable finite residue.","pith_inferences":["Beyond the paper: if the fixed point exists, the same mechanism would generate masses for all fermion families without an elementary Higgs sector, and the predicted dynamical-Higgs width could be confronted with precision collider data.","The surface-equivalence claim can be tested directly by lattice simulations that compare equal-time and null-plane quantization of the same interacting theory; a spectrum mismatch would falsify it.","The paper notes a tachyonic mass in the conformally invariant AdS5 scalar action; following the four-fermion logic, the natural extension is to look for the spontaneously broken vacuum in which that tachyon becomes a positive physical mass.","The existence of the QED fixed point is inherited from an older program rather than proven here; a direct nonperturbative computation of the beta function would decide whether the finite results are realized in a concrete theory."],"forward_implications":["Equal-time and light-front-time commutators describe one theory, so light-front results can be converted to instant-time language by a unitary change of variables in every order of perturbation theory.","Light-front vacuum tadpole graphs are nonzero and must be computed as four-dimensional off-shell Feynman diagrams including the circle-at-infinity contribution; old-fashioned on-shell perturbation theory misses them.","Mass can appear with no bare mass term: at the fixed point with $\\gamma_\\theta(\\alpha)=-1$, chiral symmetry breaks spontaneously and produces a finite dynamical fermion mass.","The dynamical Higgs boson has finite mass near the fermion mass but above its decay threshold, so it has a width; an elementary double-well Higgs would be real and widthless.","The vacuum energy can be made finite, so the cosmological constant can be controlled: the quartic divergence is assigned to conformal gravity, the quadratic divergence is downgraded to logarithmic by critical scaling, and the logarithmic remainder is cancelled by the mean-field mass term."],"supporting_citations":[{"why":"Introduces the infinite-momentum frame that the light-front approach recasts and that the paper uses as the historical starting point.","marker":"[4]"},{"why":"Introduces light-front variables and the graph classification by sign of $x^+$, the technical basis for the light-front evaluation.","marker":"[5]"},{"why":"Establishes the equality of instant-time and light-front Feynman diagrams and the unitary equivalence used here, including the Lehmann representation.","marker":"[15]"},{"why":"Shows the light-front vacuum tadpole is nonzero via the circle-at-infinity contribution, a key step for vacuum physics.","marker":"[16]"},{"why":"Derives the equality of unequal-time commutators restricted to equal $x^+$, the mechanism that identifies light-front quantization with instant-time quantization.","marker":"[20]"},{"why":"Supplies the four-fermion gap equation and the dynamical symmetry-breaking template that the paper dresses with QED.","marker":"[22]"},{"why":"Provides the fixed-point QED program whose scale-invariant propagator and anomalous dimensions the paper uses to remove the cutoff.","marker":"[25,26,27]"},{"why":"Gives the compatibility condition $\\gamma_\\theta(\\alpha)=-1$ that makes the four-fermion interaction renormalizable and the vacuum energy finite.","marker":"[28]"},{"why":"Supplies the finite Goldstone and Higgs residues and the massive Higgs width quoted in the paper.","marker":"[31]"}],"fun_headline_variants":["Light-front quantization is instant-time in disguise","Unitary transform equates light-front and instant-time commutators","Conformal breaking gives finite mass and vacuum energy","Mass from dynamical symmetry breaking at a fixed point"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument's load-bearing premise is that the quantum electromagnetic interaction has a special point—a renormalization-group fixed point—where it becomes scale invariant and the exponent that controls the fermion-pair operator is exactly minus one; if that point does not exist, the cutoff cannot be removed and the finite vacuum energy and Higgs mass results collapse.","fun_headline_variants_meta":{"raw":{"variants":["Light-front quantization is instant-time in disguise","Unitary transform equates light-front and instant-time commutators","Conformal breaking gives finite mass and vacuum energy","Mass from dynamical symmetry breaking at a fixed point"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00042,"raw_usage":{"total_tokens":2155,"prompt_tokens":932,"completion_tokens":1223,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":548,"completion_tokens_details":{"reasoning_tokens":1162}},"tokens_in":548,"tokens_out":1223,"duration_ms":247007,"temperature":1.0,"reasoning_tokens":1162,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T00:48:22.745139+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"One could settle the mass-generation claim by computing the quantum electromagnetic beta function nonperturbatively (for example, on a spacetime lattice with many fermion flavors) and checking for a fixed point with exponent $-1$. The surface-equivalence claim could be settled by discretizing the same interacting theory on equal-time and null-plane surfaces and comparing the full spectra and matrix elements; any mismatch would disprove the unitary equivalence.","supporting_citations":[{"cited_title":"Weinberg, Phys","cited_arxiv_id":null,"evidence_quote":"Introduces the infinite-momentum frame that the light-front approach recasts and that the paper uses as the historical starting point."},{"cited_title":"Chang and S","cited_arxiv_id":null,"evidence_quote":"Introduces light-front variables and the graph classification by sign of $x^+$, the technical basis for the light-front evaluation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the equality of instant-time and light-front Feynman diagrams and the unitary equivalence used here, including the Lehmann representation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows the light-front vacuum tadpole is nonzero via the circle-at-infinity contribution, a key step for vacuum physics."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Derives the equality of unequal-time commutators restricted to equal $x^+$, the mechanism that identifies light-front quantization with instant-time quantization."},{"cited_title":"Nambu and G","cited_arxiv_id":null,"evidence_quote":"Supplies the four-fermion gap equation and the dynamical symmetry-breaking template that the paper dresses with QED."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the compatibility condition $\\gamma_\\theta(\\alpha)=-1$ that makes the four-fermion interaction renormalizable and the vacuum energy finite."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the finite Goldstone and Higgs residues and the massive Higgs width quoted in the paper."}],"review_version":1}