Deformation quantization of fermi fields

Abstract

Deformation quantization for any Grassmann scalar free field is described via the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal ⋆-product and the Wigner functional are obtained by extending the formalism proposed recently in [35] to the fermionic systems of infinite number of degrees of freedom. In particular, this formalism is applied to quantize the Dirac free field. It is observed that the use of suitable oscillator variables facilitates considerably the procedure. The Stratonovich-Weyl quantizer, the Moyal ⋆-product, the Wigner functional, the normal ordering operator, and finally, the Dirac propagator have been found with the use of these variables.

Weyl–Wigner–Moyal formalism for Fermi classical systems

“…dµ 1 . The formulas (35) and (36) are similar to the corresponding formulas for the bosonic case [30,31,32].…”

“…The extension of our present considerations to the fermionic systems with an infinite number of degrees of freedom will be reported in a future communication [34]. In particular we are going to deal with deformation quantization of fermionic fields coupled to electromagnetic fields [35], [36].…”

“…In particular we are going to deal with deformation quantization of fermionic fields coupled to electromagnetic fields [35], [36].…”

Rarita-Schwinger Quantum Free Field via Deformation Quantization

“…It was shown in [14] that, for the system described by the Dirac equation (1), the time independent Schrödinger equation can be written as…”

“…The free electromagnetic field and the Dirac field were discussed in [13,14] respectively. Also some works have been done in relation to the gravitational field [15] and bosonic string theory [16].…”