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On the Weyl Quantized Relativistic Hamiltonian

Takashi Ichinose

Published Jan 1, 1992• 4 citations

Abstract

This note discusses a general condition on essential selfadjointness of the Weyl quantized relativistic Hamiltonian and the path integral representation for its semigroup. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI: 10.1007/978-3-0348-8623-9_10

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Birkhäuser Basel eBooks

On the Weyl Quantized Relativistic Hamiltonian

Takashi Ichinose

Published Jan 1, 1992• 4 citations

Publisher

Abstract

DOI: 10.1007/978-3-0348-8623-9_10

Related papers

Lecture 2: Pseudo-differential Operators. Berezin, Kohn–Nirenberg, Born–Jordan Quantizations

Gianfausto Dell’Antonio

Atlantis studies in mathematical physicsJan 1, 20160 citations

Path Integral for the Relativistic Schrödinger Semigroup

Takashi Ichinose

We consider the Weyl quantized relativistic Hamiltonian H = H A ∔Ф defined through the quadratic form corresponding to the classical symbol $\sqrt {{{{{\left( {p - A\left( x \right)} \right)}}^{2}} + {{m}^{2}}}} + \Phi \left( x \right),{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \left( {p,x} \right) \in {{\mathbb{R}}^{d}} \times {{\mathbb{R}}^{d}},$ (1.1)of a spinless particle with mass m ≥ 0 in an electromagnetic field (e.g. Landau-Lifschitz [9]), where the light velocity c is taken to be equal to 1.We consider the Weyl quantized relativistic Hamiltonian H = H A ∔Ф defined through the quadratic form corresponding to the classical symbol $ \sqrt {{{{{\left( {p - A\left( x \right)} \right)}}^{2}} + {{m}^{2}}}} + \Phi \left( x \right),{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \left( {p,x} \right) \in {{\mathbb{R}}^{d}} \times {{\mathbb{R}}^{d}}, $ (1.1)of a spinless particle with mass m ≥ 0 in an electromagnetic field (e.g. Landau-Lifschitz [9]), where the light velocity c is taken to be equal to 1.

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Stochastic PDE’s of Schrödinger Type and Stochastic Mehler Kernels — a Path Integral Approach

Aubrey Truman, Tomasz Zastawniak

Birkhäuser Basel eBooksJan 1, 19994 citations

We consider the Weyl quantized relativistic Hamiltonian H = H A ∔Ф defined through the quadratic form corresponding to the classical symbol

\sqrt {{{{{\left( {p - A\left( x \right)} \right)}}^{2}} + {{m}^{2}}}} + \Phi \left( x \right),{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} \left( {p,x} \right) \in {{\mathbb{R}}^{d}} \times {{\mathbb{R}}^{d}},

(1.1)of a spinless particle with mass m ≥ 0 in an electromagnetic field (e.g. Landau-Lifschitz [9]), where the light velocity c is taken to be equal to 1.