Poincaré symmetries and representations in pseudo-Hermitian quantum field theory

• URL: http://arxiv.org/abs/2307.16805v2
• Date: Wed, 3 Apr 2024 12:27:01 GMT
• Title: Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Authors: Esra Sablevice, Peter Millington,
• Abstract summary: This paper explores quantum field theories with pseudo-Hermitian Hamiltonians. PT-symmetric Hamiltonians serve as a special case. We extend the Poincar'e algebra to include non-Hermitian generators.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper explores quantum field theories with pseudo-Hermitian Hamiltonians, where PT-symmetric Hamiltonians serve as a special case. In specific regimes, these pseudo-Hermitian Hamiltonians have real eigenspectra, orthogonal eigenstates, and unitary time evolution. So far, most pseudo-Hermitian quantum field theories have been constructed using analytic continuation or by adding non-Hermitian terms to otherwise Hermitian Hamiltonians. However, in this paper, we take a different approach. We construct pseudo-Hermitian scalar and fermionic quantum field theories from first principles by extending the Poincar\'e algebra to include non-Hermitian generators. This allows us to develop consistent pseudo-Hermitian quantum field theories, with Lagrangian densities that transform appropriately under the proper Poincar\'e group. By doing so, we establish a more solid theoretical foundation for the emerging field of non-Hermitian quantum field theory.

Related papers

• Quantum simulation of the pseudo-Hermitian Landau-Zener-St\"uckelberg-Majorana effect [0.0]
  We present a quantum simulation of the time-dependent non-Hermitian non-PT-symmetric Hamiltonian used in a pseudo-Hermitian extension of the Landau-Zener-St"uckelberg-Majorana (LZSM) model.
  arXiv  Detail & Related papers  (2024-01-30T20:53:44Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory [0.0]
  We consider a prototype model containing a single Dirac fermion with a parity-odd, anti-Hermitian mass term. In the phase of unbroken PT symmetry, this Dirac fermion model is equivalent to a Hermitian theory under a similarity transformation.
  arXiv  Detail & Related papers  (2022-01-26T17:12:36Z)
• $\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
  Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
  arXiv  Detail & Related papers  (2021-03-27T09:46:36Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
  We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
  arXiv  Detail & Related papers  (2020-09-24T18:00:13Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories [0.0]
  We discuss second quantization, discrete symmetry transformations and inner products in free non-Hermitian quantum field theories with PT symmetry. We focus on a prototype model of two complex scalar fields with anti-Hermitian mass mixing.
  arXiv  Detail & Related papers  (2020-06-11T17:48:51Z)
• The Non-Hermitian quantum mechanics and its canonical structure [7.784991832712813]
  The non-Hermitian Schr"odinger equation is re-expressed generally in the form of Hamilton's canonical equation without any approximation. The conventional difficulties in non-Hermitian quantum mechanics are totally overcome by the reformulation.
  arXiv  Detail & Related papers  (2020-05-21T05:52:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.