Two novel proofs establish equivalence between path integral and stochastic quantizations for scalar Euclidean QFTs via forest-indexed Taylor interpolations.
Renormalization of phi**4 theory on noncommutative R**4 in the matrix base
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abstract
We prove that the real four-dimensional Euclidean noncommutative \phi^4-model is renormalisable to all orders in perturbation theory. Compared with the commutative case, the bare action of relevant and marginal couplings contains necessarily an additional term: an harmonic oscillator potential for the free scalar field action. This entails a modified dispersion relation for the free theory, which becomes important at large distances (UV/IR-entanglement). The renormalisation proof relies on flow equations for the expansion coefficients of the effective action with respect to scalar fields written in the matrix base of the noncommutative R^4. The renormalisation flow depends on the topology of ribbon graphs and on the asymptotic and local behaviour of the propagator governed by orthogonal Meixner polynomials.
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Computes UV-finite noise spectra in interferometers from graviton fluctuations in vacuum/thermal/squeezed states and from massless scalar vacuum stress-energy, all Planck-suppressed.
Quantum spacetime with a non-commutative dual explains the fixed Born rule of quantum theory and leads to gravitized quantum mechanics featuring dynamical probabilities and higher-order interference.
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From path integral quantization to stochastic quantization: a pedestrian's journey
Two novel proofs establish equivalence between path integral and stochastic quantizations for scalar Euclidean QFTs via forest-indexed Taylor interpolations.
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Geometric noise spectrum in interferometers
Computes UV-finite noise spectra in interferometers from graviton fluctuations in vacuum/thermal/squeezed states and from massless scalar vacuum stress-energy, all Planck-suppressed.
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Quantum Spacetime, Quantum Gravity and Gravitized Quantum Theory
Quantum spacetime with a non-commutative dual explains the fixed Born rule of quantum theory and leads to gravitized quantum mechanics featuring dynamical probabilities and higher-order interference.