Causal Construction of the Massless Vertex Diagram

Aste, Andreas

doi:10.1007/s11005-006-0113-3

Cited by 1 publication

(2 citation statements)

References 11 publications

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“…In this work, for simplicity, we will always express these parameters in the laboratory frame. Finally, the condition of permeability in terms of the physical strengths can now be written in covariant form by multiplying (53) at the left by S L and at the right by S −1 L , which does not change the determinant (54), and results in the covariantly permeability condition :…”

Section: Lorentz Covariant Form Of Dirac Equation With a General Pimentioning

confidence: 99%

“…The use of distribution theory to deal with singularities is well-known in quantum field theory, where the causal approach, introduced by Epstein and Glaser in [50] and further developed by Scharf [51] and collaborators, has been applied to many physical systems/problems (see, e.g. [52][53][54][55] and references therein). In one-dimensional quantum mechanics, the distributional approach provides a mathematically rigorous method that allows us to write the interaction explicitly in terms of the Dirac spinor, ψ(x), and the parameters characterizing the b.c.…”

Section: Introductionmentioning

confidence: 99%

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The physical interpretation of point interactions in one-dimensional relativistic quantum mechanics

Bonin,

Lunardi,

Manzoni

2024

J. Phys. A: Math. Theor.

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We investigate point interactions in one-dimensional relativistic quantum mechanics using a distributional approach based on Schwartz's theory of distributions. From the properties of the most general covariant distribution describing relativistic point interactions we obtain the physical parameters associated with the point potentials that behave as a scalar, a pseudo-scalar and a vector under Lorentz transformations. Then, we establish a one-to-one relationship between these physical parameters and the well-known set of four parameters giving the boundary conditions at the singular point(s), which define a self-adjoint Hamiltonian. By considering the non-relativistic limit, we obtain the most general point interaction in the Schr"odinger equation in terms of these four physical point potentials. Finally, we study the symmetries of the relativistic point interactions under space inversion, time reversal and charge conjugation, and investigate how requirements of invariance under these symmetry transformations can be used to restrict the set of physical parameters.

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Section: Lorentz Covariant Form Of Dirac Equation With a General Pimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The physical interpretation of point interactions in one-dimensional relativistic quantum mechanics

Bonin,

Lunardi,

Manzoni

2024

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

Causal Construction of the Massless Vertex Diagram

Abstract: Abstract. The massless one-loop vertex diagram is constructed by exploiting the causal structure of the diagram in configuration space, which can be translated directly into dispersive relations in momentum space.

Cited by 1 publication

References 11 publications

The physical interpretation of point interactions in one-dimensional relativistic quantum mechanics

The physical interpretation of point interactions in one-dimensional relativistic quantum mechanics

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