E=Mc2 Versus Symmetry for Lorentz Covariant Physics

Kong, Otto C. W.; Ting, Hock King

doi:10.2139/ssrn.4266951

Cited by 2 publications

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“…Such a description of quantum dynamics, while available since at least around 1940 [6,7] (see for example the books of [8,9] and references therein), is not what is commonly presented in textbooks. Even the 'standard' presentation of classical Hamiltonian dynamics does not do that (see however Johns [10]) and hence does not give a Lorentz covariant formulation [5]. Our results here also illustrate an advantage of that formulation of 'relativistic' dynamics, classical and quantum.…”

Section: Introductionmentioning

confidence: 75%

“…The last section gives careful discussions of various related aspects of the theory of quantum mechanics. While the Heisenberg picture analysis is not dependent on the explicit theory for the corresponding, even abstract vector space, Schrödinger picture, our new theory of 'relativistic' quantum mechanics with a notion of Minkowski metric operator for the vector space of states [5,11], defining the inner product, is conceptually deeply connected to our Heisenberg picture results. In particular, we emphasize a perspective that takes seriously the quantum observables as physical quantities to be understood beyond the framework of classical physical concepts.…”

Section: Introductionmentioning

confidence: 86%

“…where m is effectively a Casimir invariant for the irreducible representation to be interpreted as Newtonian mass [5]. An abstract Fock state basis as well as coherent state wavefunction description of that has been essentially presented [5,11]. What is particularly interesting to note, in relation to the present analysis, is that the theory has a representation space that is Krein, instead of Hilbert.…”

Section: More About the Quantum Theorymentioning

confidence: 96%

Section: More About the Quantum Theorymentioning

confidence: 99%

“…We used the 'nonrelativistic' setting to clarify the key background perspective above for a good reason. Our preferred 'relativistic' theory for dynamics is one with an invariant evolution parameter s in the place of Newtonian time [5]. For all the classical analyses here, the solution gives the particle proper time as a linear function of the s parameter, hence essentially identifying the two physically.…”

Section: Introductionmentioning

confidence: 99%

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Equivalence principle for quantum mechanics in the Heisenberg picture

Kong

2024

Class. Quantum Grav.

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We present an exact quantum observable analog of the weak equivalence principle for a `relativistic' quantum particle. The quantum geodesic equations are obtained from Heisenberg equations of motion as an exact analog of a fully covariant classical Hamiltonian evolution picture, with the proper identification of the canonical momentum variables as $p_\mu$, rather than $p^\mu$. We discuss the meaning of the equations in relation to projective measurements as well as equations with solution curves as ones in the noncommutative geometric picture of spacetime, and a plausible approach to quantum gravity as a theory about quantum observables as physical quantities including the notion of quantum coordinate transformation.

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Section: Introductionmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 86%

Section: More About the Quantum Theorymentioning

confidence: 96%

Section: More About the Quantum Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Equivalence principle for quantum mechanics in the Heisenberg picture

Kong

2024

Class. Quantum Grav.

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Special Relativity and Its Newtonian Limit from a Group Theoretical Perspective

Kong

Payne

2021

Symmetry

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In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting point of the formulation is the representations of the relativity symmetries. Moreover, that seriously furnishes—via the notion of symmetry contractions—a natural way in which one can understand how the Newtonian theory arises as an approximation to Einstein’s theory. We begin with the Poincaré symmetry underlying special relativity and the nature of Minkowski spacetime as a coset representation space of the algebra and the group. Then, we proceed to the parallel for the phase space of a spin zero particle, in relation to which we present the full scheme for its dynamics under the Hamiltonian formulation, illustrating that as essentially the symmetry feature of the phase space geometry. Lastly, the reduction of all that to the Newtonian theory as an approximation with its space-time, phase space, and dynamics under the appropriate relativity symmetry contraction is presented. While all notions involved are well established, the systematic presentation of that story as one coherent picture fills a gap in the literature on the subject matter.

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E=Mc2 Versus Symmetry for Lorentz Covariant Physics

Cited by 2 publications

References 0 publications

Equivalence principle for quantum mechanics in the Heisenberg picture

Equivalence principle for quantum mechanics in the Heisenberg picture

Special Relativity and Its Newtonian Limit from a Group Theoretical Perspective

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