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Register a new userThe Master Ward Identity for scalar QED
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Added by
Karl-Henning Rehren
Publication date
2020
fields
Physics
and research's language is
English
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It is emphasized that for interactions with derivative couplings, the Ward Identity (WI) securing the preservation of a global U(1) symmetry should be modified. Scalar QED is taken as an explicit example. More precisely, it is rigorously shown in scalar QED that the naive WI and the improved Ward Identity (Master Ward Identity, MWI) are related to each other by a finite renormalization of the time-ordered product (T-product) for the derivative fields; and we point out that the MWI has advantages over the naive WI - in particular with regard to the proof of the MWI. We show that the MWI can be fulfilled in all orders of perturbation theory by an appropriate renormalization of the T-product, without conflict with other standard renormalization conditions. Relations with other recent formulations of the MWI are established.
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The present work tackles the existence of local gauge symmetries in the setting of Algebraic Quantum Field Theory (AQFT). The net of causal loops, previously introduced by the authors, is a model independent construction of a covariant net of local C*-algebras on any 4-dimensional globally hyperbolic spacetime, aimed to capture some structural properties of any reasonable quantum gauge theory. In fact, representations of this net can be described by causal and covariant connection systems, and the local gauge transformations arise as maps between equivalent connection systems. The present paper completes these abstract results, realizing QED as a representation of the net of causal loops in Minkowski spacetime. More precisely, we map the quantum electromagnetic field F{mu}{ u}, not free in general, into a representation of the net of causal loops and show that the corresponding connection system and local gauge transformations find a counterpart in terms of F{mu}{ u}.
We propose a three-dimensional electromagnetic current operator within light-front dynamics that satisfies a light-front Ward-Takahashi identity for two-fermion systems. The light-front current operator is obtained by a quasi-potential reduction of the four-dimensional current operator and acts on the light-front valence component of bound or scattering states. A relation between the light-front valence wave function and the four-dimensional Bethe-Salpeter amplitude both for bound or scattering states is also derived, such that the matrix elements of the four-dimensional current operator can be fully recovered from the corresponding light-front ones. The light-front current operator can be perturbatively calculated through a quasi-potential expansion, and the divergence of the proposed current satisfies a Ward-Takahashi identity at any given order of the expansion. In the quasi-potential expansion the instantaneous terms of the fermion propagator are accounted for by the effective interaction and two-body currents. We exemplify our theoretical construction in the Yukawa model in the ladder approximation, investigating in detail the current operator at the lowest nontrivial order of the quasi-potential expansion of the Bethe-Salpeter equation. The explicit realization of the light-front form of the Ward-Takahashi identity is verified. We also show the relevance of instantaneous terms and of the pair contribution to the two-body current and the Ward-Takahashi identity.
The worldline formalism has previously been used for deriving compact master formulas for the one-loop N-photon amplitudes in both scalar and spinor QED, and in the vacuum as well as in a constant external field. For scalar QED, there is also an analogous master formula for the propagator dressed with N photons in the vacuum. Here, we extend this master formula to include a constant field. The two-photon case is worked out explicitly, yielding an integral representation for the Compton scattering cross section in the field suitable for numerical integration in the full range of electric and magnetic field strengths.
In these notes we review the field-theoretical approach to the computation of the scalar product of multi-magnon states in the Sutherland limit where the magnon rapidities condense into one or several macroscopic arrays. We formulate a systematic procedure for computing the 1/M expansion of the on-shell/off-shell scalar product of M-magnon states in the generalised integrable model with SU(2)-invariant rational R-matrix. The coefficients of the expansion are obtained as multiple contour integrals in the rapidity plane.
The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico and Zerbini [9,10,51] have considered some configurations involving delta-type potentials concentrated at points of $mathbb{R}^3$; in particular, the case with an isolated point singularity at the origin can be formulated as a field theory on $mathbb{R}^3setminus {mathbf{0}}$, with self-adjoint boundary conditions at the origin for the Laplacian. However, the above authors have discussed only global aspects of the Casimir effect, focusing their attention on the vacuum expectation value (VEV) of the total energy. In the present paper we analyze the local Casimir effect with a point delta-type potential, computing the renormalized VEV of the stress-energy tensor at any point of $mathbb{R}^3setminus {mathbf{0}}$; to this purpose we follow the zeta regularization approach, in the formulation already employed for different configurations in previous works of ours (see [29-31] and references therein).
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