Intrinsic gravitational regularization of quantum fields

One implication of maximal proper acceleration is an intrinsic regularization of quantum fields which depends on the universal gravitational constant. It also follows that the vacuum energy density, seen by any one observer, is finite.     

Off-shell fields and pauli-villars regularization

We analyze the correspondence between a five-dimensional U(1)gauge invariant theory and four-dimensional scalar QED, where the fifth dimension ()is an invariant parameter of evolution of the manifestly covariant one-particle sector as well as for the full Fock space. The correspondence is represented by the limit in which the width of the photon mass distribution s tends to zero and large correlations occur. In the limiting procedure, calculation of a twopoint diagram shows that the PauliVillars regularization is intrinsically related to these longrange correlations.     

Continuum regularization of quantum field theory

As a complement to our earlier study of renormalization at the Langevin regularized level, we report here on equivalent renormalization programs for regularized Schwinger-Dyson systems. Both one-loop and iterated loop renormalizations of the Green functions of QCD₄ are given, and are shown to be equivalent to the Langevin results. The optional apparent ?-renormalization discussed in IV is shown to apply as well to Schwinger-Dyson systems as to Langevin systems.     

Stochastic regularization of quantum field theory

The equivalence between a D-dimensional classical field theory coupled to an external random source having Gaussian correlations and its D−2 dimensional quantum counterpart was established. Utilizing this equivalence, a regularization procedure for scalar theories is developed. The regularization amounts to a compacification of the extra two dimensions. The regularization scheme is interpreted in terms of superpropagator modifications.     

Continuum regularization of quantum field theory

As an extension of our earlier one-loop renormalization studies at the regularized Schwinger-Dyson level, we report here on equivalent renormalization programs for regularized Langevin systems. Proper structure is discussed, and proper one-loop renormalizations of the Green functions of φ ₆ ³ and QCD₄ are given. An optional apparent?-renormalization is discussed as a technical simplificaiton for gauge theories with Zwanziger's gauge-fixing.     

Infrared regularization for spin-1 fields

We extend the method of infrared regularization to spin-1 fields. As applications, we discuss the chiral extrapolation of the rho meson mass from lattice QCD data and the pion-rho sigma term.Received: 18 November 2004, Published online: 4 February 2005PACS: 12.39.Fe, 12.38.GcWork supported in part by Deutsche Forschungsgemeinschaft through grants provided for the SFB/TR 16 Subnuclear Structure of Matter.     

Infrared regularization in two-dimensional quantum chromodynamics

Using 2-dimensional quantum chromodynamics as an example, it is shown that the gauge-invariant fields formalism allows one to avoid the difficulties related to the choice of an infrared regularization, and leads to confinement of both single quarks and quark-antiquark pairs.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 74–78, May, 1990.     

Noninvariant zeta-function regularization in quantum Liouville theory

We consider two possible zeta-function regularization schemes of quantum Liouville theory. One refers to the Laplace–Beltrami operator covariant under conformal transformations, the other to the naive noninvariant operator. The first produces an invariant regularization which however does not give rise to a theory invariant under the full conformal group. The other is equivalent to the regularization proposed by A.B. Zamolodchikov and Al.B. Zamolodchikov and gives rise to a theory invariant under the full conformal group.     

Dimensional regularization of massless quantum electrodynamics in spherical spacetime

The quantization and renormalization of massless electrodynamics in a spacetime of constant curvature are discused. A formalism is presented which is valid in an arbitrary number of dimensions and therefore allows the use of dimensional regularization. In the discussion of the photon propagator it is found that anomalous mass terms dependent on the curvature arise, although these vanish in four dimensions. Further, the gauge-fixing term in the Lagrangian has the unconventional feature of not being a perfect square. The renormalizability of the theory is then demonstrated to one loop order, and the renormalization constants are shown to retain their flat spacetime values. Finally, expansions for the renormalized electron and photon propagators in terms of appropriate spherical harmonics are derived.     

On fermi quantum fields constructed from bose quantum fields and their applications

In former papers a representation of the quantum Fermi and para-Fermi fields was proposed. This representation is such that the only basic quantum entities are Bose quantum fields. In this paper we show several possibilities of application: (i) to lower the number of elementary particles; (ii) to describe as separate states of a fundamental particle other particles that presently are considered as different, and to induce an ordering among them; (iii) to obtain relations among the quantum numbers of those particles; (iv) to obtain a physical picture of some unstable particles. This article is concerned with the physical interpretation of the formalism, and some of the statements that are contained here have a conjectural character.     

Renormalisation of out-of-equilibrium quantum fields

We consider the initial value problem and its renormalisation in the framework of the two-particle-irreducible (2PI) effective action. We argue that in the case of appropriately chosen self-consistent initial conditions, the counterterms needed to renormalise the system in equilibrium are also sufficient to renormalise its time evolution. In this way we improve on Gaussian initial conditions which have the disadvantage of generically not showing a continuum limit. For a more detailed discussion see [Sz. Borsányi and U. Reinosa, arXiv:0809.0496].     

A class of quantum fields constructed from Markoff fields

A class of fields with the mass parameter is constructed from Gaussian fields. The procedure of linearization of the Hamiltonian is shown to be equivalent to some linear transformation on the space indexing the Gaussian process.     

Random fields and quantum dynamics

We shall discuss quantum mechanical operators depending on the time or on the manifold in space. There is a similarity to the case of stochastic processes or random fields, where the innovation approach is one of the powerful tools to investigate their probabilistic structure. Having had some review of the innovation, similar attempt is made for some cases in quantum dynamics.