Ryusuke Endo

GENERAL SOLUTION OF THE QUANTUM DAMPED HARMONIC OSCILLATOR

In this paper the general solution of the quantum damped harmonic oscillator is given.

Gaugeon Formalism for Spin-3/2 Rarita-Schwinger Gauge Field

We apply the BRST symmetric gaugeon formalism to the spin-3/2 Rarita-Schwinger gauge field. To this time, this formalism has been developed for quantum electrodynamics and the Yang-Mills gauge field. The theory admits a quantum gauge transformation by which we can shift the gauge fixing parameter. The quantum gauge transformation does not change the BRST charge. Thus, the physical Hilbert space is trivially independent of the gauge fixing parameter. By virtue of the BRST symmetry, the physical Hilbert space is still well-defined when we incorporate the interaction with the Ricci flat background gravitational field.

BRST Symmetric Gaugeon Formalism for the Higgs Model

We reinvestigate Yokoyama’s gaugeon formalism for the spontaneously broken Abelian gauge theory. Within the framework of the covariant linear gauges, we give a general gaugefixing Lagrangian which includes the gauge field, the Goldstone mode, the multiplier B-field and Yokoyama’s gaugeon fields (as well as Faddeev-Popov ghosts). As special choices of the values of the gauge-fixing parameters, our theory includes the usual covariant gauges and Rξ-like gauges. Although some of the gauge-fixing parameters can be shifted by the q-number gauge transformation, the ξ parameter cannot be shifted in any of the Rξ-like gauges.

An Extension of Type I Gaugeon Formalism for Quantum Electrodynamics

By introducing two kinds of gaugeon fields, we extend Yokoyamas Type I gaugeon formalism for quantum electrodynamics. The theory admits a q-number gauge transformation by which we can shift the gauge parameter into arbitrary numerical value; whereas in the original theory we cannot change the sign of the parameter. The relation to the Type II theory is also discussed

Gauge Freedom in Path Integrals in Abelian Gauge Theory

Abstract We extend gauge symmetry of Abelian gauge field to incorporate quantum gauge degrees of freedom. We twice apply the Harada–Tsutsui gauge recovery procedure to gauge-fixed theories. First, starting from the Faddeev–Popov path integral in the Landau gauge, we recover the gauge symmetry by introducing an additional field as an extended gauge degree of freedom. Fixing the extended gauge symmetry by the usual Faddeev–Popov procedure, we obtain the theory of Type I gaugeon formalism. Next, applying the same procedure to the resulting gauge-fixed theory, we obtain a theory equivalent to the extended Type I gaugeon formalism.

Gaugeon formalism for the second-rank antisymmetric tensor gauge fields

We present a BRST symmetric gaugeon formalism for the two-form gauge fields. A set of vector gaugeon fields is introduced as a quantum gauge freedom. One of the gaugeon fields satisfies a higher derivative field equation; this property is necessary to change the gauge-fixing parameter of the two-form gauge field. A naive Lagrangian for the vector gaugeon fields is itself invariant under a gauge transformation for the vector gaugeon field. The Lagrangian of our theory includes the gauge-fixing terms for the gaugeon fields and corresponding Faddeev--Popov ghosts terms.