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Kinematical Condition for Spontaneous Chiral- and Gauge-Symmetry Breaking : An interpretation of Brout-Englert-Higgs mechanism

Shun-ichiro Koh

Abstract

A new interpretation of the Brout-Englert-Higgs (BEH) mechanism is proposed. Since all material particles have their own masses, the place in which massless fermions and antifermions exist is a hypothetical world. Since physical quantities of massless particles are not positive definite, gauge field does not distinguish between annihilation of massless fermion and creation of massless antifermion with opposite momentum and spin, which leads to a vacuum different from the Fock vacuum. However this hypothetical world is not exactly realized. Whatever effective interaction acts on massless fermion, it comes back on fermion and antifermion as an inertial mass. Massless fermion and antifermion are generated as pairs, and they behave as quasi bosons. Due to Bose statistics, their direction of motion is made parallel to each other, and their transverse excitations are suppressed by an energy gap, which makes the gauge boson massive. The dynamic part of the above effective interaction induces a Higgs-like excitation. This interpretation explains the origin of the vacuum condensate, and sheds a new light on the BEH mechanism.

Kinematical Condition for Spontaneous Chiral- and Gauge-Symmetry Breaking : An interpretation of Brout-Englert-Higgs mechanism

Abstract

A new interpretation of the Brout-Englert-Higgs (BEH) mechanism is proposed. Since all material particles have their own masses, the place in which massless fermions and antifermions exist is a hypothetical world. Since physical quantities of massless particles are not positive definite, gauge field does not distinguish between annihilation of massless fermion and creation of massless antifermion with opposite momentum and spin, which leads to a vacuum different from the Fock vacuum. However this hypothetical world is not exactly realized. Whatever effective interaction acts on massless fermion, it comes back on fermion and antifermion as an inertial mass. Massless fermion and antifermion are generated as pairs, and they behave as quasi bosons. Due to Bose statistics, their direction of motion is made parallel to each other, and their transverse excitations are suppressed by an energy gap, which makes the gauge boson massive. The dynamic part of the above effective interaction induces a Higgs-like excitation. This interpretation explains the origin of the vacuum condensate, and sheds a new light on the BEH mechanism.

Paper Structure

This paper contains 16 sections, 68 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Hypothetical world
  3. Kinematical condition
  4. The vacuum of hypothetical world
  5. The behavior as Quasi bosons
  6. Relativistic quantum field in position space
  7. Statistical gap
  8. Massive gauge boson
  9. Gauge-boson's mass due to statistical gap
  10. Goldstone mode
  11. Higgs particle
  12. Discussion
  13. Comparison to the BEH model
  14. Further implications
  15. The vacuum $|\widetilde{0}\rangle$ satisfying $\widetilde{a}^s(\hbox{\boldmath $p$})|\widetilde{0}\rangle =\widetilde{b}^s(-\hbox{\boldmath $p$})|\widetilde{0}\rangle =0$
  16. ...and 1 more sections

Figures (2)

  • Figure 1: A schematic view of the physical vacuum at a certain moment in position space. Each white circle represents a quasi-boson, which is distributed with a mean distance $d_m$. (a) The transverse displacements ($dr$) of quasi bosons from the horizontal line ($z$ axis) are coupled to the gauge field $B_{\mu}$ propagating along the $z$ axis, and (b) the longitudinal displacements ($dz$) are illustrated.
  • Figure 2: The coherent space-time region is the inside of a small light-cone specified by $l_c$ (a shaded area). (a) The gauge boson $B_{\mu}$ (a wavy line) induces vacuum polarization only outside this region. (b) The chain of creation and annihilation of fermion-antifermion pairs constitutes the Higgs-like excitation $H(x)$, which is induced both inside and outside this region .