Nonperturbative calculation of symmetry breaking in quantum field theory

Bender, Carl M.; Milton, Kimball A.

doi:10.1103/physrevd.55.r3255

Cited by 113 publications

(144 citation statements)

References 14 publications

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“…This equivalence can be realized when the coordinate paths for the repulsive interaction are taken along a curve in the complex space [1,2] . Recently this kind of relationship between Hermitian and non-Hermitian oscillator systems has attracted much attention [3,4] in the search for examples of PT-symmetric non-Hermitian quantum Hamiltonians with real spectra [2,5,6,7].…”

Section: Introductionmentioning

confidence: 99%

Dual oscillators and quantum pendulums: Spectrum and correlators

Andrianov

2007

Phys. Rev. D

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We outline the nonlinear transformation in the path integral representation for partition function of O(N ) symmetric oscillator systems bringing their duality to certain one-dimensional oscillators with unstable potential shapes. This duality transformation realizes the equivalence between spectra of a Hermitian and a nonHermitian Hamiltonians. It is exploited to calculate exactly the spectra of quantum rotators . The zero-temperature limit is considered and the dual representation of n-point correlators of coordinate operators is obtained.

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Section: Introductionmentioning

confidence: 99%

Dual oscillators and quantum pendulums: Spectrum and correlators

Andrianov

2007

Phys. Rev. D

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“…The chosen or "input" Hamiltonian H is allowed to be non-Hermitian in the Dirac sense, H = H † . Bender and Boettcher's [5] PT −symmetric oscillator H (BB) = p 2 + gx 2 with g = g(x) = (ix) δ and δ > 0 serves as an often quoted example. Still, characterizing the PTQT models primarily as non-Hermitian would be misleading.…”

Section: The Formalismmentioning

confidence: 99%

“…where the anti-linear operator T mediates the reversal of time [5]. The model is given its full physical content by a self-consistent construction of a second observable, viz., of the operator of charge C = C (P T ) (H) [3,6].…”

Section: The Formalismmentioning

confidence: 99%

Smeared quantum lattices exhibiting 𝒫𝒯‐symmetry with positive 𝒫

Znojil¹,

Geyer²

2012

Fortschritte der Physik

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A new strategy of the use of 𝒫𝒯 symmetry in quantum theory is proposed. The essence of the innovation lies in the replacement of the usual parity‐like choice of 𝒫 by its non‐involutory and positive‐definite alternative 𝒫(positive) ≠ I. The resulting modified concept of 𝒫(positive)𝒯‐symmetry remains phenomenologically appealing as well as technically useful. This is demonstrated and illustrated via an N‐site quantum lattice model which is exactly solvable in terms of Legendre polynomials.

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“…In 1996, following a rather large number of precursors, it began to be recognized that perhaps the usual requirement of Hermiticity of the Hamiltonian was overly restrictive [1]. Theories [2] and proved in 2001 [3,4].…”

Section: Introductionmentioning

confidence: 99%

“…It was soon recognized, however, that this theory would not be renormalizable because of anomalies (the electric current was an axial vector); but then another version of PT QED was proposed [9] with an ordinary vector current interaction, but with anomalous transformation properties under parity. 1 The C operator, in lowest order, was constructed the following year [11], which should guarantee the unitarity of the theory. However, that has proved extraordinarily difficult to establish [12].…”

Section: Introductionmentioning

confidence: 99%

PT -symmetric quantum electrodynamics and unitarity

Milton

Abalo

Parashar

et al. 2013

Phil. Trans. R. Soc. A.

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More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, . It was shown that, if is unbroken, energies were, in fact, positive, and unitarity was satisfied. Since quantum mechanics is quantum field theory in one dimension—time—it was natural to extend this idea to higher-dimensional field theory, and in fact an apparently viable version of -invariant quantum electrodynamics (QED) was proposed. However, it has proved difficult to establish that the unitarity of the scattering matrix, for example, the Källén spectral representation for the photon propagator, can be maintained in this theory. This has led to questions of whether, in fact, even quantum mechanical systems are consistent with probability conservation when Green’s functions are examined, since the latter have to possess physical requirements of analyticity. The status of QED will be reviewed in this paper, as well as the general issue of unitarity.

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Nonperturbative calculation of symmetry breaking in quantum field theory

Cited by 113 publications

References 14 publications

Dual oscillators and quantum pendulums: Spectrum and correlators

Dual oscillators and quantum pendulums: Spectrum and correlators

Smeared quantum lattices exhibiting 𝒫𝒯‐symmetry with positive 𝒫

PT -symmetric quantum electrodynamics and unitarity

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