Euclidean formulation of relativistic quantum mechanics of N particles
- URL: http://arxiv.org/abs/2010.10944v1
- Date: Tue, 20 Oct 2020 15:27:50 GMT
- Title: Euclidean formulation of relativistic quantum mechanics of N particles
- Authors: Gohin Shaikh Samad and W.N.Polyzou
- Abstract summary: Euclidean formulation of relativistic quantum mechanics for systems of a finite number of degrees of freedom is discussed.
Theory can be formulated entirely in the Euclidean representation without the need for analytic continuation.
Explicit formulas for generators of the Poincar'e group for any spin are constructed and shown to be self-adjoint on the Euclidean representation of the Hilbert space.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A Euclidean formulation of relativistic quantum mechanics for systems of a
finite number of degrees of freedom is discussed. Relativistic treatments of
quantum theory are needed to study hadronic systems at sub-hadronic distance
scales. While direct interaction approaches to relativistic quantum mechanics
have proved to be useful, they have two disadvantages. One is that cluster
properties are difficult to realize for systems of more than two particles. The
second is that the relation to quantum field theories is indirect. Euclidean
formulations of relativistic quantum mechanics provide an alternative
representation that does not have these difficulties. More surprising, the
theory can be formulated entirely in the Euclidean representation without the
need for analytic continuation. In this work a Euclidean representation of a
relativistic $N$-particle system is discussed. Kernels for systems of N free
particles of any spin are given and shown to be reflection positive. Explicit
formulas for generators of the Poincar\'e group for any spin are constructed
and shown to be self-adjoint on the Euclidean representation of the Hilbert
space. The structure of correlations that preserve both the Euclidean
covariance and reflection positivity is discussed.
Related papers
- Semiclassical gravity phenomenology under the causal-conditional quantum measurement prescription II: Heisenberg picture and apparent optical entanglement [13.04737397490371]
In quantum gravity theory, a state-dependent gravitational potential introduces nonlinearity into the state evolution.
The formalism for understanding the continuous quantum measurement process on the quantum state has been previously discussed using the Schr"odinger picture.
In this work, an equivalent formalism using the Heisenberg picture is developed and applied to the analysis of two optomechanical experiment protocols.
arXiv Detail & Related papers (2024-11-08T14:07:18Z) - Entanglement in dual unitary quantum circuits with impurities [0.0]
We investigate entanglement dynamics in a quantum circuit perturbed by an impurity.
We compute entanglement entropy for both a semi-infinite and a finite subsystem within a finite distance of the impurity.
We show that such non-monotonic behavior can arise even in random chaotic circuits.
arXiv Detail & Related papers (2024-10-04T13:57:01Z) - Antiparticles in non-relativistic quantum mechanics [55.2480439325792]
Non-relativistic quantum mechanics was originally formulated to describe particles.
We show how the concept of antiparticles can and should be introduced in the non-relativistic case without appealing to quantum field theory.
arXiv Detail & Related papers (2024-04-02T09:16:18Z) - Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders [9.617349193925188]
Entanglement constitutes one of the key concepts in quantum mechanics and serves as an indispensable tool in the understanding of quantum many-body systems.
We perform extensive numerical investigations of extensive entanglement properties of coupled quantum spin chains.
arXiv Detail & Related papers (2023-11-03T04:06:20Z) - Fluctuations, uncertainty relations, and the geometry of quantum state
manifolds [0.0]
The complete quantum metric of a parametrized quantum system has a real part and a symplectic imaginary part.
We show that for a mixed quantum-classical system both real and imaginary parts of the quantum metric contribute to the dynamics.
arXiv Detail & Related papers (2023-09-07T10:31:59Z) - Stochastic Mechanics and the Unification of Quantum Mechanics with
Brownian Motion [0.0]
We show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a process that is rotated in the complex plane.
We then extend this theory to relativistic theories on integrals using the framework of second order geometry.
arXiv Detail & Related papers (2023-01-13T10:40:27Z) - On the collective properties of quantum media [0.0]
We discuss the hydrodynamic representation of a wide class of quantum media exhibiting similar elementary excitations and dispersion properties.
The representation covers quantum systems characterized by any type of (long-range) self-interaction, associated with an arbitrary potential.
It also accounts for possible nonlinearities, which may arise e.g., due to short-range interactions (collisions) in the case of bosons, or from the Pauli exclusion principle for fermions.
arXiv Detail & Related papers (2022-09-12T06:17:24Z) - Genuine multipartite entanglement and quantum coherence in an
electron-positron system: Relativistic covariance [117.44028458220427]
We analyze the behavior of both genuine multipartite entanglement and quantum coherence under Lorentz boosts.
A given combination of these quantum resources is shown to form a Lorentz invariant.
arXiv Detail & Related papers (2021-11-26T17:22:59Z) - Fully Symmetric Relativistic Quantum Mechanics and Its Physical
Implications [0.0]
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime.
The reformulation requires that time and space, as well as the timelike and spacelike intervals, are treated equally, which makes the new theory fully symmetric and consistent with the Special Theory of Relativity.
arXiv Detail & Related papers (2021-05-31T19:13:19Z) - Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
Two particles are identical if all their intrinsic properties, such as spin and charge, are the same.
Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles.
We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
arXiv Detail & Related papers (2021-05-10T13:11:59Z) - Quantum particle across Grushin singularity [77.34726150561087]
We study the phenomenon of transmission across the singularity that separates the two half-cylinders.
All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection.
This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
arXiv Detail & Related papers (2020-11-27T12:53:23Z)
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.