A proper scalar product for tachyon representations in configuration space

• URL: http://arxiv.org/abs/2007.12608v1
• Date: Fri, 24 Jul 2020 16:08:33 GMT
• Title: A proper scalar product for tachyon representations in configuration space
• Authors: Francisco F. L\'opez-Ruiz, Julio Guerrero and Victor Aldaya
• Abstract summary: We propose a new inner product for scalar fields that are solutions of the Klein-Gordon equation with $m20$. This inner product is non-local, bearing an integral kernel including Bessel functions of the second kind. This new scenario suggests a revision of the corresponding quantum field theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new inner product for scalar fields that are solutions of the Klein-Gordon equation with $m^2<0$. This inner product is non-local, bearing an integral kernel including Bessel functions of the second kind, and the associated norm proves to be positive definite in the subspace of oscillatory solutions, as opposed to the conventional one. Poincar\'e transformations are unitarily implemented on this subspace, which is the support of a unitary and irreducible representation of the proper orthochronous Poincar\'e group. We also provide a new Fourier Transform between configuration and momentum spaces which is unitary, and recover the projection onto the representation space. This new scenario suggests a revision of the corresponding quantum field theory.

Related papers

• Reproducing Kernel Hilbert Space Approach to Non-Markovian Quantum Stochastic Models [0.0]
  We give a derivation of the non-Markovian quantum state diffusion equation of Di'osi and Strunz. We show that the complex trajectories arises as a consequence of using the Bargmann-Segal representation of the bath.
  arXiv  Detail & Related papers  (2024-07-09T21:10:54Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space [49.1574468325115]
  We find an exceptional point at a critical dissipation strength that separates oscillating and non-oscillating decay. We also describe a different type of dissipation that leads to a single decay mode in the whole operator subspace.
  arXiv  Detail & Related papers  (2024-05-27T16:11:39Z)
• A metaplectic perspective of uncertainty principles in the Linear Canonical Transform domain [0.0]
  We derive Heisenberg uncertainty principles for pairs of Linear Canonical Transforms of a given function. We also propose a new quadratic phase-space distribution, which represents a signal along two intermediate directions in the time-frequency plane.
  arXiv  Detail & Related papers  (2024-05-17T09:26:48Z)
• Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
  The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
  arXiv  Detail & Related papers  (2022-10-15T13:53:21Z)
• Integral Quantization for the Discrete Cylinder [0.456877715768796]
  We show how to derive corresponding covariant integral quantizations from (weight) functions on the phase space. We also look at the specific cases of coherent states built from shifted gaussians, Von Mises, Poisson, and Fej'er kernels.
  arXiv  Detail & Related papers  (2022-08-19T21:23:43Z)
• Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spaces [52.424621227687894]
  We introduce a unified framework for group equivariant networks on homogeneous spaces. We take advantage of the sparsity of Fourier coefficients of the lifted feature fields. We show that other methods treating features as the Fourier coefficients in the stabilizer subgroup are special cases of our activation.
  arXiv  Detail & Related papers  (2022-06-16T17:59:01Z)
• Linear Classifiers in Mixed Constant Curvature Spaces [40.82908295137667]
  We address the problem of linear classification in a product space form -- a mix of Euclidean, spherical, and hyperbolic spaces. We prove that linear classifiers in $d$-dimensional constant curvature spaces can shatter exactly $d+1$ points. We describe a novel perceptron classification algorithm, and establish rigorous convergence results.
  arXiv  Detail & Related papers  (2021-02-19T23:29:03Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)

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.