The stepwise path integral of the relativistic point particle

Koch, Benjamin; Muñoz, Enrique

doi:10.1140/epjc/s10052-018-5753-9

Cited by 6 publications

(12 citation statements)

References 32 publications

(102 reference statements)

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“…(b) Local Lorentz invariance: This means that the Lagrangian is invariant under local rotations and boosts of the vector (dx µ )/(dλ) at any point along the trajectory. A formal argument on why this symmetry, which is not a classical gauge symmetry, is important in this given context was presented in [21][22][23]. In [21] it was further shown in the Hamiltonian action formulation that there is a non-trivial constraint associated with this symmetry.…”

Section: B the Relativistic Point Particlementioning

confidence: 99%

“…A naive, straightforward definition of a path integral for the relativistic point particle fails to satisfy the Kolmogorov condition for transition probability amplitudes. As shown in [21][22][23], this is due to the overcounting arising from the symmetries b), and c), that needs to be properly factored out either by geometric considerations [21,22] or by a group theoretical analysis involving the Fadeev-Popov method [23].…”

Section: General Considerations On the Explicit Form Of The Pi Measurementioning

confidence: 99%

“…• A PI over the Hamiltonian action and the corresponding constraint analysis [21] • A direct PI in Euclidean space [22] • A formal functional path integral [23] These results were either obtained in Euclidean space or with abstract formal methods, but a detailed analysis of the much richer structure of Minkowski space is missing.…”

Section: Introduction a The Contextmentioning

confidence: 99%

“…The notation of this introduction closely follows Ref. [22]. In the next section, the quantization procedure will be realized.…”

Section: Introduction a The Contextmentioning

confidence: 99%

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Path integral of the relativistic point particle in Minkowski space

Koch,

Muñoz

2020

Preprint

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In this article, we analyze the fundamental global and local symmetries involved in the action for the free relativistic point particle. Moreover, we identify a hidden local symmetry, whose explicit consideration and factorization utilizing of a Fujikawa prescription, leads to the construction of relativistic propagators that satisfy the Chapman-Kolmogorov identity. By means of a detailed topological analysis, we find three different relativistic propagators (orthochronous, space-like, and Feynman) which are obtained from the exclusive integration of paths within different sectors in Minkowski space. Finally, the connection of this approach to the Feynman checkerboard construction is explored. Contents I. Introduction A. The context B. The relativistic point particle C. General considerations on the explicit form of the PI measure II. The propagator A. Action B. The two step propagator C. The N + 1 step propagator D. Space-like, time-like, orthochronous, and the Feynman propagator E. Comparison to the propagators of the Klein-Gordon field F. Without spatial flip symmetry and Feynmans' checkerboard G. Higher dimensional generalization of the propagator H. Higher dimensional generalization of the checkerboard? III. Conclusion Acknowlegements Appendix References

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Section: B the Relativistic Point Particlementioning

confidence: 99%

Section: General Considerations On the Explicit Form Of The Pi Measurementioning

confidence: 99%

Section: Introduction a The Contextmentioning

confidence: 99%

“…The notation of this introduction closely follows Ref. [22]. In the next section, the quantization procedure will be realized.…”

Section: Introduction a The Contextmentioning

confidence: 99%

See 2 more Smart Citations

Path integral of the relativistic point particle in Minkowski space

Koch,

Muñoz

2020

Preprint

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“…Thus, δx µ reflects the spirit of the velocity rotations in the Lagrangian formulation [12,13]. The constraint further generates a variation of the action…”

Section: The Algebra Of Local Transformationsmentioning

confidence: 99%

A hidden constraint on the Hamiltonian formulation of relativistic worldlines

Koch

Muñoz

2019

Eur. Phys. J. C

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Gauge theories with general covariance are particularly reluctant to quantization. We discuss the example of the Hamiltonian formulation of the relativistic point particle that, despite its apparent simplicity, is of crucial importance since a number of point particle systems can be cast into this form on a higher dimensional Rindler background, as recently pointed out by Hojman. It is shown that this system can be equipped with a hidden local, symmetry generating, constraint which on the one hand does not bother the classical evolution and on the other hand simplifies the realization of the path integral quantization. Even though the positive impact of the hidden symmetry is more evident in the Lagrangian version of the theory, it is still present through the suggested Hamiltonian constraint.

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Path integral of the relativistic point particle in Minkowski space

Koch

Muñoz

2021

Phys. Rev. D

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The stepwise path integral of the relativistic point particle

Cited by 6 publications

References 32 publications

Path integral of the relativistic point particle in Minkowski space

Path integral of the relativistic point particle in Minkowski space

A hidden constraint on the Hamiltonian formulation of relativistic worldlines

Path integral of the relativistic point particle in Minkowski space

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