A Goldstone theorem in thermal relativistic quantum field theory

Jäkel, Christian; Wreszinski, Walter F.

doi:10.1063/1.3526961

Cited by 1 publication

(2 citation statements)

References 32 publications

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“…As discussed in [11], no direct particle interpretation can be inferred from (44). Actually, the singularity inĜ n can be proved to exist only at p = 0 and not on the whole null cone.…”

Section: Proof Of the Goldstone Theoremmentioning

confidence: 97%

“…Based on the analysis of Swieca [69], a proof of the Goldstone theorem without using Lorentz invariance has been given by Morchio and Strocchi in [54], see also the book [65] for the application of similar ideas for the analysis of the case of finite temperature. Furthermore, the analysis of the slow decay of large spatially separated correlation functions in the presence of spontaneous symmetry breaking is discussed in [44]. However, when a nontrivial background is present as for the case of Bose-Einstein condensation, we don't expect that the presence of a gapless mode is directly related to the clustering properties of the correlation functions for large spatial separation.…”

Section: Spontaneous Symmetry Breaking and The Goldstone Theoremmentioning

confidence: 99%

See 1 more Smart Citation

Algebraic Approach to Bose–Einstein Condensation in Relativistic Quantum Field Theory: Spontaneous Symmetry Breaking and the Goldstone Theorem

Brunetti

Fredenhagen

Pinamonti

2020

Ann. Henri Poincaré

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We construct states describing Bose–Einstein condensates at finite temperature for a relativistic massive complex scalar field with $$|\varphi |^4$$ | φ | 4 -interaction. We start with the linearized theory over a classical condensate and construct interacting fields by perturbation theory. Using the concept of thermal masses, equilibrium states at finite temperature can be constructed by the methods developed in Fredenhagen and Lindner (Commun Math Phys 332:895, 2014) and Drago et al. (Ann Henri Poincaré 18:807, 2017). Here, the principle of perturbative agreement plays a crucial role. The apparent conflict with Goldstone’s theorem is resolved by the fact that the linearized theory breaks the U(1) symmetry; hence, the theorem applies only to the full series but not to the truncations at finite order which therefore can be free of infrared divergences.

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“…As discussed in [11], no direct particle interpretation can be inferred from (44). Actually, the singularity inĜ n can be proved to exist only at p = 0 and not on the whole null cone.…”

Section: Proof Of the Goldstone Theoremmentioning

confidence: 97%