Preconjugate variables in quantum field theory and their applications

Abstract

Preconjugate variables X have commutation relations with the energy-momentum P of the respective system which are of a more general form than just the Hamiltonian one. Since they have been proven useful in their own right for finding new spacetimes we present here a study of them. Interesting examples can be found via geometry: motions on the mass-shell for massive and massless systems, and via group theory: invariance under special conformal transformations of mass-shell, resp. light-cone -both find representations on Fock space. We work mainly in ordinary fourdimensional Minkowski space and spin zero. The limit process from non-zero to vanishing mass turns out to be non-trivial and leads naturally to wedge variables. We point out some applications and extension to more general spacetimes. In a companion paper we discuss the transition to conjugate pairs. 1

Conjugate variables in quantum field theory and a refinement of Pauli’s theorem

“…Group theoretic considerations in section 3 serve to recapitulate earlier work [22], then to find a place for non-commutative coordinates, but in particular -via some new interpretation on Fock space -to control our derivations there. The distinguished role played by the special conformal generators as the only preconjugate X's which are local in position space and permit a smooth transition between off-shell and on-shell had been pointed out already in [28]. This explains why in the group theoretic context they have been singled out.…”

“…It turns out that due to the presence of the polarization vectors this commutator does not vanish. When searching for non-commutative coordinates one may thus rely on preconjugate pairs [28], one may introduce Θ's like in (10) or one can employ the operators Q (eff ) , (45). We hope to come back to this question in the near future.…”

“…of (11) which still yields interesting results [28], but in the present paper we will study the full strength of (11) on states in Fock space and its surrounding system of Green functions. From all preconjugate operators introduced in [28] we will consider here in detail: X(∇), X(<) and X(K) being based on the mass shell belonging to four-dimensional Minkowski space and X(< 0 ), X(K) being based on (1, 1) + (0, 2)-dimensional spacetime. The preconjugate X(ω) does not lead to Lorentz covariant Q on (1, 3)-dimensional spacetime and is therefore discarded.…”

Survey on deep learning methods in human action recognition

“…However, there is no satisfactory solution which can be effectively used in different applications such as object recognition in scenes, human action recognition, and behaviour recognition in complex, large-scale data. According to the studies, real environments contributed to a small range of studies due to inefficient feature extraction methods [47][48][49][50], while a wide range of applications for human action recognition occurs in real out door environments.…”

A Poincaré covariant noncommutative spacetime

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We interpret, in the realm of relativistic quantum field theory, the tangential operator given by Coleman, Mandula [CM67] (see also [MPS16]) as an appropriate coordinate operator. The investigation shows that the operator generates a Snyder-like noncommutative spacetime with a minimal length that is given by the mass.

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