High Energy Physics - Theory · arXiv:1204.4653 v2 · submitted 20 Apr 2012
Remarks on the thermodynamics and the vacuum energy of a quantum Maxwell gas on compact and closed manifolds
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“Using zeta-function regularization the free energy is determined and the effect of the topology of the spatial manifold on the vacuum energy and on the thermal gauge field excitations is clarified.”
from the abstract · picked out as the main claim by a classifier
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Abstract
The quantum Maxwell theory at finite temperature at equilibrium is studied on compact and closed manifolds in both the functional integral- and Hamiltonian formalism. The aim is to shed some light onto the interrelation between the topology of the spatial background and the thermodynamic properties of the system. The quantization is not unique and gives rise to inequivalent quantum theories which are classified by {\theta}-vacua. Based on explicit parametrizations of the gauge orbit space in the functional integral approach and of the physical phase space in the canonical quantization scheme, the Gribov problem is resolved and the equivalence of both quantization schemes is elucidated. Using zeta-function regularization the free energy is determined and the effect of the topology of the spatial manifold on the vacuum energy and on the thermal gauge field excitations is clarified. The general results are then applied to a quantum Maxwell gas on a n-dimensional torus providing explicit formulae for the main thermodynamic functions in the low- and high temperature regimes, respectively.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.22 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| The quantum Maxwell theory at finite temperature at equilibrium is studied on compact and closed manifolds in both the functional integral- and Hamiltonian formalism. | contribution 0.88 | 0.84 | 0.04 | asserted 0.99 |
| The aim is to shed some light onto the interrelation between the topology of the spatial background and the thermodynamic properties of the system. | contribution 0.54 | 0.27 | 0.06 | unclear 0.51 |
| The quantization is not unique and gives rise to inequivalent quantum theories which are classified by {\theta}-vacua. | result 0.48 | 0.46 | 0.09 | asserted 1.00 |
| Based on explicit parametrizations of the gauge orbit space in the functional integral approach and of the physical phase space in the canonical quantization scheme, the Gribov problem is resolved and the equivalence of both quantization schemes is elucidated. | method 0.47 | 0.92 | 0.20 | asserted 1.00 |
| Using zeta-function regularization the free energy is determined and the effect of the topology of the spatial manifold on the vacuum energy and on the thermal gauge field excitations is clarified. | result 0.65 | 0.93 | 0.30 | asserted 1.00 |
| The general results are then applied to a quantum Maxwell gas on a n-dimensional torus providing explicit formulae for the main thermodynamic functions in the low- and high temperature regimes, respectively. | result 0.60 | 0.93 | 0.27 | asserted 1.00 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00
What was examined, and what was not
Sources read
- arXiv listing abstract v2
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- full text
- figures and tables
- references and citing sentences
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- P abstract
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- S sections
- T body sentences
- C citations
- R cross-paper relations
How the labels were made
Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,053 input tokens, $0.0002 reported.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
How the literature uses it
2 arXiv papers cite this in 8 sentences
Papers citing it · 5 sentences without a confident label
Compares with it 1 paper
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[ref] in the presence of the electric fluxes.
Maxwell Theory on a Compact Manifold as a Topologically Ordered System · Degeneracy at $θ_eff=π$ · 0.95
Cites it as background 1 paper
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More recently, the computations for the electromagnetic field on general manifolds were explicitly done in [ref] , and papers referenced therein.
Topological Casimir effect in Maxwell Electrodynamics on a Compact Manifold · Introduction. Motivation. · 0.92
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