Functional integrals and inequivalent representations in Quantum Field Theory

Blasone, Massimo; Jizba, Petr; Smaldone, L. A.

doi:10.1016/j.aop.2017.05.022

Cited by 16 publications

(22 citation statements)

References 62 publications

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“…The properly chosen measure for this integration d d−1 N o,i is Ω i . Note that this adjustment of the measure is not unusual, since it is known that canonical transformations, similar to those generated by N µ o,i , can result in a change of the path integral measure [14][15][16].…”

Section: E Path Integralmentioning

confidence: 93%

A hidden constraint on the Hamiltonian formulation of relativistic worldlines

Koch

Muñoz

2019

Eur. Phys. J. C

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Gauge theories with general covariance are particularly reluctant to quantization. We discuss the example of the Hamiltonian formulation of the relativistic point particle that, despite its apparent simplicity, is of crucial importance since a number of point particle systems can be cast into this form on a higher dimensional Rindler background, as recently pointed out by Hojman. It is shown that this system can be equipped with a hidden local, symmetry generating, constraint which on the one hand does not bother the classical evolution and on the other hand simplifies the realization of the path integral quantization. Even though the positive impact of the hidden symmetry is more evident in the Lagrangian version of the theory, it is still present through the suggested Hamiltonian constraint.

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Section: E Path Integralmentioning

confidence: 93%

A hidden constraint on the Hamiltonian formulation of relativistic worldlines

Koch

Muñoz

2019

Eur. Phys. J. C

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“…In Refs. [7], in particular, it was found that the vacuum for fields with definite mass (mass vacuum) is unitarily inequivalent [9,10] to the one for fields with definite flavor (flavor vacuum), as they are related by a non-trivial Bogoliubov transformation. In light of this, it is reasonable to expect that vacuum effects in the context of QFT mixing may, in principle, depend on which of these states represents the physical vacuum.…”

Section: Introductionmentioning

confidence: 99%

Casimir effect for mixed fields

et al. 2018

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We analyze the Casimir effect for a flavor doublet of mixed scalar fields confined inside a one-dimensional finite region. In the framework of the unitary inequivalence between mass and flavor representations in quantum field theory, we employ two alternative approaches to derive the Casimir force: in the first case, the zero-point energy is evaluated for the vacuum of fields with definite mass, then similar calculations are performed for the vacuum of fields with definite flavor. We find that signatures of mixing only appear in the latter context, showing the result to be independent of the mixing parameters in the former.

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“…On the other hand, if we set β = 0, α = 0 and put t 2 = t , t 1 = t, we obtain the Green's function (16) in the explicit form…”

Section: I(t −T) + θ(T − T )E I(t −T) (54)mentioning

confidence: 99%

“…There, the problem of the non-invariance of the vacuum state is particularly pressing because ensuing vacuum states typically belong to different (unitarily inequivalent) Hilbert spaces [2,3,11,14]. This situation shows up, e.g., in quantum systems with spontaneous symmetry breaking (SSB) [14][15][16], in cases where renormalization issues are relevant [3,[16][17][18] or in the study of flavor mixing both in flat [3,19] and curved backgrounds [20]. The latter point has lead recently to phenomenologically relevant correction to the standard neutrino oscillation formula [21].…”

Section: Introductionmentioning

confidence: 99%

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Generalized generating functional for mixed-representation Green's functions: A quantum-mechanical approach

2017

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When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes. Here we propose a generalized generating functional for Green's functions which allows to easily distinguish among a continuous set of vacua that are mutually connected via unitary canonical transformations. In order to keep our discussion as simple as possible, we limit ourselves to Quantum Mechanics where the generating functional of Green's functions is constructed by means of phase-space path integrals. The quantum-mechanical setting allows to accentuate the main logical steps involved without embarking on technical complications such as renormalization or inequivalent representations that should otherwise be addressed in the full-fledged Quantum Field Theory. We illustrate the inner workings of the generating functional obtained by discussing Green's functions among vacua that are mutually connected via translations and dilatations. Salient issues, including connection with Quantum Field Theory, vacuum-to-vacuum transition amplitudes and perturbation expansion in the vacuum parameter are also briefly discussed.

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Functional integrals and inequivalent representations in Quantum Field Theory

Cited by 16 publications

References 62 publications

A hidden constraint on the Hamiltonian formulation of relativistic worldlines

A hidden constraint on the Hamiltonian formulation of relativistic worldlines

Casimir effect for mixed fields

Generalized generating functional for mixed-representation Green's functions: A quantum-mechanical approach

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