Non-relativistic tachyons: a new representation of the Galilei group

• URL: http://arxiv.org/abs/2407.15466v2
• Date: Thu, 25 Jul 2024 11:49:49 GMT
• Title: Non-relativistic tachyons: a new representation of the Galilei group
• Authors: Victor Aldaya, Julio Guerrero, Francisco F. López-Ruiz,
• Abstract summary: We arrive at a consistent, nonstandard representation of the Galilei group. The corresponding quantum (and classical) theory shares with the relativistic one their fundamentals. The tachyonic objects described by the new representation cannot be regarded as localizable in the standard sense.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An algebraic characterization of the contractions of the Poincar\'e group permits a proper construction of a non-relativistic limit of its tachyonic representation. We arrive at a consistent, nonstandard representation of the Galilei group which was disregarded long ago by supposedly unphysical properties. The corresponding quantum (and classical) theory shares with the relativistic one their fundamentals, and serves as a toy model to better comprehend the unusual behavior of the tachyonic representation. For instance, we see that evolution takes place in a spatial coordinate rather than time, as for relativistic tachyons, but the modulus of the three-momentum is the same for all Galilean observers, leading to a new dispersion relation for a Galilean system. Furthermore, the tachyonic objects described by the new representation cannot be regarded as localizable in the standard sense.

Related papers

• Galilean Relativity and the Path Integral Formalism in Quantum Mechanics [0.0]
  In quantum mechanics Galilean boosts require a non-trivial transformation rule for the wave function. The representation of certain symmetry groups in quantum mechanics can be simply understood in terms of the transformation properties of the classical Lagrangian.
  arXiv  Detail & Related papers  (2023-06-23T13:09:19Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Non-Gaussian superradiant transition via three-body ultrastrong coupling [62.997667081978825]
  We introduce a class of quantum optical Hamiltonian characterized by three-body couplings. We propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model.
  arXiv  Detail & Related papers  (2022-04-07T15:39:21Z)
• Projective representation of the Galilei group for classical and quantum-classical systems [0.0]
  A unitary irreducible non-projective representation of the Galilei group is possible in the Koopman-von Neumann formulation of classical mechanics. We show, by direct construction, that classical mechanics also allows for a projective representation of the Galilei group where the mass is the central charge of the algebra.
  arXiv  Detail & Related papers  (2021-07-08T06:25:39Z)
• Unitary representation of the Poincar\'e group for classical relativistic dynamics [0.0]
  We give a unitary irreducible representation of the Poincar'e group that leads to an operational version of the classical relativistic dynamics of a massive spinless particle. Unlike quantum mechanics, in this operational theory there is no uncertainty principle between position and momentum.
  arXiv  Detail & Related papers  (2021-05-28T14:44:55Z)
• 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)
• Group Theoretical Approach to Pseudo-Hermitian Quantum Mechanics with Lorentz Covariance and $c \rightarrow \infty $ Limit [0.0]
  The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation. The key feature of the formulation is that it is not unitary but pseudo-unitary, exactly in the same sense as the Minkowski spacetime representation. Explicit wavefunction description is given without any restriction of the variable domains, yet with a finite integral inner product.
  arXiv  Detail & Related papers  (2020-09-12T23:48:52Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• Lorentz Group Equivariant Neural Network for Particle Physics [58.56031187968692]
  We present a neural network architecture that is fully equivariant with respect to transformations under the Lorentz group. For classification tasks in particle physics, we demonstrate that such an equivariant architecture leads to drastically simpler models that have relatively few learnable parameters.
  arXiv  Detail & Related papers  (2020-06-08T17:54:43Z)
• Emergence of classical behavior in the early universe [68.8204255655161]
  Three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another.
  arXiv  Detail & Related papers  (2020-04-22T16:38:25Z)
• Covariant Quantum Mechanics and Quantum Spacetime [0.0]
  The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation. Explicit wavefunction description is given without any restriction of the variable domains, yet with a finite integral inner product.
  arXiv  Detail & Related papers  (2020-02-04T08:55:56Z)

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.