Conformal 3-Point Functions and the Lorentzian OPE in Momentum Space

In conformal field theory in Minkowski momentum space, the 3-point correlation functions of local operators are completely fixed by symmetry. Using Ward identities together with the existence of a Lorentzian operator product expansion (OPE), we show that the Wightman function of three scalar operators is a double hypergeometric series of the Appell $$F_4$$ F 4 type. We extend this simple closed-form expression to the case of two scalar operators and one traceless symmetric tensor with arbitrary spin. Time-ordered and partially-time-ordered products are constructed in a similar fashion and their relation with the Wightman function is discussed.

From Green function to quantum field

A pedagogical introduction to the theory of a Gaussian scalar field which shows firstly, how the whole theory is encapsulated in the Wightman function [Formula: see text] regarded abstractly as a two-index tensor on the vector space of (spacetime) field configurations, and secondly how one can arrive at [Formula: see text] starting from nothing but the retarded Green function [Formula: see text]. Conceiving the theory in this manner seems well suited to curved spacetimes and to causal sets. It makes it possible to provide a general spacetime region with a distinguished “vacuum” or “ground state”, and to recognize some interesting formal relationships, including a general condition on [Formula: see text] expressing zero-entropy or “purity”.

Scalar and fermion representations of the Lorentz group in Minkowski plane, QFT correlators, pair creation in electric field and the Unruh effect

Boost modes [Formula: see text] are eigenfunctions of the Lorentz transformations generator in two-dimensional (2D) Minkowski space (MS). We demonstrate and discuss deep interrelation between the boost modes and the field correlators, also known as Wightman functions. In the case of a massive scalar field, the boost modes, as functions of the spectral parameter [Formula: see text], contain the Dirac delta-function singularity [Formula: see text] at the light cone. The zero boost mode coincides up to a constant factor with the Wightman function. The light cone singularity of boost modes for a fermion field is stronger. For this case, they contain the Gelfand [Formula: see text]-function of complex argument [Formula: see text], while the Wightman function components coincide with analytical continuation of the boost modes set towards the spectral values [Formula: see text]. We argue that due to the discovered properties of the boost modes the so-called Unruh modes, which are at the core of the Unruh effect derivation, do not constitute a complete set in MS and thus cannot be used for quantization of neither scalar, nor fermion field. Finally, we discuss boost modes for the case of the constant electric background and rederive the well-known result for spontaneous pair creation rate. Solution of this problem in the boost modes representation reveals distinctions between the Unruh problem and the effect of pair creation by an electric field in vacuum.

UNIFORMLY ACCELERATED DETECTOR IN THE κ-DEFORMED DIRAC VACUUM

In this paper, we investigate how a uniformly accelerated detector responds to vacuum state of a Dirac field in the κ-Minkowski spacetime. Starting from κ-deformed Dirac theory, which is invariant under κ-Poincaré algebra, we derive κ-deformed Wightman function for Dirac field, which is valid up to first-order in the deformation parameter a. Using this, we calculate the response function of the uniformly accelerated detector, which is coupled to massless Dirac field in κ-spacetime. From this, we obtain the modification to Unruh effect for the κ-deformed Dirac field, valid up to first-order in the deformation parameter.