Phases of quartic scalar theories and PT symmetry

• URL: http://arxiv.org/abs/2409.05439v2
• Date: Wed, 04 Dec 2024 16:34:12 GMT
• Title: Phases of quartic scalar theories and PT symmetry
• Authors: Leqian Chen, Sarben Sarkar,
• Abstract summary: We show that the conjecture is true for the real part of the ground state energy and of the excited state energies. The analogous relation for partition functions in zero spacetime dimensions is valid for many cases. The possibility that the conjecture is valid, for a single component field theory in higher dimensional spacetimes, is discussed.
• Score: 0.0
• License:
• Abstract: For quantum mechanical anharmonic oscillator-type Hamiltonians, it is shown that there is a relation between the energy eigenvalues of parity symmetric and PT-symmetric phases for weak coupling. The possibility of such a relation was conjectured by Ai, Bender and Sarkar on examining the imaginary part of the ground state energy using path integrals. In the weak coupling limit, we show that the conjecture is true also for the real part of the ground state energy and of the excited state energies. However, the conjecture is false for strong coupling. The analogous relation for partition functions in zero spacetime dimensions is valid for many cases. However $O(N)$ symmetric multi-component scalar fields, with $N>1$ and a quartic interaction, do not satisfy the conjecture for zero and one dimensional spacetime. The possibility that the conjecture is valid, for a single component field theory in higher dimensional spacetimes, is discussed in a simplified model.

Related papers

• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• Theory of Complex Particle without Extra Dimensions [0.0]
  Critical dimension of the complex particle in Minkowski spacetime is $D = 4$, while $D = 2, 4$ or $6$ are permitted in Euclid spacetime. The origin of the restriction to the dimension is the existence of tertiary constraint in the canonical theory, quantization.
  arXiv  Detail & Related papers  (2024-07-02T03:25:13Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory III: Bosonic and Fermionic Negativity [0.0]
  We study the resolved R'enyi entropies of quasi-particle excited states in quantum field theory. We compute the ratio of charged moments of the partially transposed reduced density matrix as an expectation value of twist operators. We find that although the operation of partial transposition requires a redefinition for fermionic theories, the ratio of the negativity moments between an excited state and the ground state is universal and identical for fermions and bosons.
  arXiv  Detail & Related papers  (2023-02-06T10:05:58Z)
• Parity-time symmetric holographic principle [0.0]
  A spinless relativistic quantum particle traveling in (1+1)-dimensional space-time is simulated under a $mathcalPT$-symmetric Hamiltonian. Our work finds the application of $mathcalPT$-symmetric and non-Hermitian physics in quantum simulation.
  arXiv  Detail & Related papers  (2022-10-03T18:00:00Z)
• Shape Invariant Potentials in Supersymmetric Quantum Cosmology [0.0]
  shape invariant potentials is an essential feature in many settings of $N=2$ supersymmetric quantum mechanics. We show how shape in property can be employed to bring a relation among several factor orderings choices for our Schr"odinger-Wheeler-DeWitt equation.
  arXiv  Detail & Related papers  (2022-05-31T19:51:21Z)
• Non-zero momentum requires long-range entanglement [6.018940870331878]
  We show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum. The statement can also be generalized to fermion systems.
  arXiv  Detail & Related papers  (2021-12-13T19:00:04Z)
• $\PT$ 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)
• Mesoscopic quantum superposition states of weakly-coupled matter-wave solitons [58.720142291102135]
  We establish quantum features of an atomic soliton Josephson junction (SJJ) device. We show that the SJJ-model in quantum domain exhibits unusual features due to its effective nonlinear strength proportional to the square of total particle number. We have shown that the obtained quantum state is more resistant to few particle losses from the condensates if tiny components of entangled Fock states are present.
  arXiv  Detail & Related papers  (2020-11-26T09:26:19Z)
• The Geometry of Time in Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We continue the study of nonrelativistic quantum gravity associated with a family of Ricci flow equations. This topological gravity is of the cohomological type, and it exhibits an $cal N=2$ extended BRST symmetry. We demonstrate a standard one-step BRST gauge-fixing of a theory whose fields are $g_ij$, $ni$ and $n$, and whose gauge symmetries consist of (i) the topological deformations of $g_ij$, and (ii) the ultralocal nonrelativistic limit of space
  arXiv  Detail & Related papers  (2020-11-12T06:57:10Z)
• 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)

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.