Spin in Quantum Field Theory

Forte, Stefano

doi:10.1007/3-540-38592-4_3

Cited by 3 publications

(3 citation statements)

References 12 publications

(21 reference statements)

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“…The approach can be readily extended to incorporate path integral representations for non-scalar particles [61,62,63,64,65]. It can also handle massless particles, though it is not so straightforward to deal properly with the resulting gauge symmetries [59] and non-Abelian interactions.…”

Section: Discussionmentioning

confidence: 99%

Foundations of a spacetime path formalism for relativistic quantum mechanics

Seidewitz

2006

Journal of Mathematical Physics

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Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative firstquantized formulation can be given for relativistic quantum mechanics, based on the parametrized paths of particles in spacetime. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such a spacetime approach has proved particularly useful in the study of quantum gravity and cosmology. This paper shows how a spacetime path formalism can be considered to arise naturally from the fundamental principles of the Born probability rule, superposition, and Poincaré invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches in the literature, relating, in particular, "off-shell" theories to traditional on-shell quantum field theory. It reproduces the results of perturbative quantum field theory for free and interacting particles, but provides intriguing possibilities for a natural program for regularization and renormalization. Further, an important consequence of the formalism is that a clear probabilistic interpretation can be maintained throughout, with a natural reduction to non-relativistic quantum mechanics.

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Section: Discussionmentioning

confidence: 99%

Foundations of a spacetime path formalism for relativistic quantum mechanics

Seidewitz

2006

Journal of Mathematical Physics

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“…A complete proof of the theorem is given in [15] and [11] provides some simple explanation of the proof. Here, we briefly explain the proof which is given in those references.…”

Section: An Informal Introduction To Homotopy Theorymentioning

confidence: 99%

Homotopy and Path Integrals

Suzuki¹

2011

Preprint

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This is an introductory review of the connection between homotopy theory and path integrals, mainly focus on works done by Schulman [23] that he compared path integral on SO(3) and its universal covering space SU (2), DeWitt and Laidlaw [15] that they proved the theorem to the case of path integrals on the multiply-connected topological spaces. Also, we discuss the application of the theorem in Aharonov-Bohm effect given by [20,24]. An informal introduction to homotopy theory is provided for readers who are not familiar with the theory.

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“…There have been several approaches proposed in the literature for extending the path integral formulation of the relativistic scalar propagator [3,4,5,6] to the case of nonscalar particles, particularly spin-1/2 (see, for example, [7,8,9,10,11]). These approaches generally proceed by including in the path integral additional variables to represent higher spin degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Spacetime path formalism for massive particles of any spin

Seidewitz¹

2009

Annals of Physics

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Earlier work presented a spacetime path formalism for relativistic quantum mechanics arising naturally from the fundamental principles of the Born probability rule, superposition, and spacetime translation invariance. The resulting formalism can be seen as a foundation for a number of previous parameterized approaches to relativistic quantum mechanics in the literature. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such approaches have proved particularly useful in the study of quantum gravity and cosmology.The present paper extends the foundational spacetime path formalism to include massive, nonscalar particles of any (integer or half-integer) spin. This is done by generalizing the principle of translational invariance used in the scalar case to the principle of full Poincaré invariance, leading to a formulation for the nonscalar propagator in terms of a path integral over the Poincaré group.Once the difficulty of the non-compactness of the component Lorentz group is dealt with, the subsequent development is remarkably parallel to the scalar case. This allows the formalism to retain a clear probabilistic interpretation throughout, with a natural reduction to non-relativistic quantum mechanics closely related to the well known generalized Foldy-Wouthuysen transformation.

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Spin in Quantum Field Theory

Cited by 3 publications

References 12 publications

Foundations of a spacetime path formalism for relativistic quantum mechanics

Foundations of a spacetime path formalism for relativistic quantum mechanics

Homotopy and Path Integrals

Spacetime path formalism for massive particles of any spin

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