Equal-time Anti-commutation Relations Research Articles

Quantum scale invariant gravity in the de Donder gauge

We perform the manifestly covariant quantization of a scale invariant gravity with a scalar field, which is equivalent to the well-known Brans-Dicke gravity via a field redefinition of the scalar field, in the de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance. First, without specifying the expression of a gravitational theory, we write down various equal-time (anti-)commutation relations (ETCRs), in particular, those involving the Nakanishi-Lautrup field, the FP ghost, and the FP antighost only on the basis of the de Donder gauge condition. It is shown that choral symmetry, which is a Poincar${\rm{\acute{e}}}$-like $IOSp(8|8)$ supersymmetry, can be derived from such a general action with the de Donder gauge. Next, taking the scale invariant gravity with a scalar field as a classical theory, we derive the ETCRs for the gravitational sector involving the metric tensor and scalar fields. Moreover, we account for how scale symmetry is spontaneously broken in quantum gravity, thereby showing that the dilaton is a massless Nambu-Goldstone particle.

Baryon number violation and novel canonical anti-commutation relations

The possible neutron–antineutron oscillation is described by an effective quadratic Lagrangian analogous to the BCS theory. It is shown that the conventional equal-time anti-commutation relations of the neutron variable n(t,x→) are modified by the baryon number violating terms. This is established by the Bjorken–Johnson–Low prescription and also by the canonical quantization combined with equations of motion. This novel canonical behavior can give rise to an important physical effect, which is illustrated by analyzing the Lagrangian that violates the baryon number but gives rise to the degenerate effective Majorana fermions and thus no neutron–antineutron oscillation. Technically, this model is neatly treated using a relativistic analogue of the Bogoliubov transformation.

On the non-relativistic limit of a spin- [formula omitted] particle in a classical gravitational field

An external gravitational field modifies the description of a spin- 1 2 particle in various ways. For instance, the inner product of Dirac wave functions, and the equal-time anti-commutation relations and the canonical energy-momentum tensor of the quantized Dirac field are modified. This has the following consequences. The Dirac-Hamiltonian (2.29) of a spin- 1 2 particle in a time-dependent gravitational field is not Hermitian. Furthermore, the Euler-Lagrange equation and the Heisenberg equation for the quantized Dirac field are not consistent. We obviate these deficiencies by the introduction of the η-field as the fundamental variable instead of the Dirac field. At the same time, the non-relativistic limit is most conveniently discussed in the η-description. For this purpose, we introduce a modification of the Foldy-Wouthuysen transformation.

Consistent Formulation of Fermions on a Minkowski Lattice

The finite-element approach described in a previous paper approximates the operator Dirac equation on a lattice in such a way that the equal-time anticommutation relations are exactly maintained. Moreover, the approximation preserves unitarity (and chiral invariance in the massless theory) and there is no fermion doubling.

Quantization of a Spin-3/2 Field Interacting with the Electromagnetic Field

Quantization of the Rarita-Schwinger field interacting with the internal (external) electro­ magnetic field is made by using the Dirac-Casalbuoni method. The generators of the Poincare group are explicitly given when the electromagnetic field is quantized. The com­ mutator of the symmetric energy-momentum densities is also obtained. When the external electromagnetic field is coupled to the Rarita-Schwinger field, some of the constraint equations have explicit time-dependence. We develop the Dirac formalism for the system with time­ dependent constraints. The result turns out to be that the J ohnson-Sudarshan disease associated with the equal-time anti-commutation relations still exists, so far the electromagnetic field is coupled through the minimal interaction.

Spontaneous creation of massive spin half particles by a rotating block hole

The techniques of second quantization in Kerr metric for the scalar and neutrino (massless) fields are extended to the massive spin half case. The normal modes of Dirac field in Kerr metric are obtained in Chandrasekhar’s representation and the field is quantized as usual by imposing equal-time anti-commutation relations. The vacuum expectation value of energy-momentum tensor is evaluated asymptotically, leading to the result that a Kerr black hole spontaneously creates, in addition to scalar and neutrino quanta, massive Dirac particles in the classical superradiant modes.

On the spinor rank of Fermi fields

We show that any Wightman field satisfying equal-time anti-commutation relations involving space derivatives of degree at mostr must have spinor rankr + 1.

Cancellation of Infinities in Second-Order Radiative Corrections in Unified Gauge Theories

Using configuration-space techniques, and assuming canonical equal-time anticommutation relations for quark fields, we exhibit a simple and direct verification of Weinberg's finiteness condition for second-order radiative corrections in unified gauge theories with the strong interactions accounted for to all orders.