On Parametrized General Relativity

A physical framework has been proposed which describes manifestly covariant relativistic evolution using a scalar time . Studies in electromagnetism, measurement, and the nature of time have demonstrated that in this framework, electromagnetism must be formulated in terms of -dependent fields. Such an electromagnetic theory has been developed. Gravitation must also use of -dependent fields, but many references do not take the metric's dependence on fully into account. Others differ markedly from general relativity in their formulation. In contrast, this paper outlines steps towards a -dependent classical intrinsic formulation of gravitation, patterned after general relativity, which we call parametrized general relativity (PGR). Given the existence of a preferred foliation, the Hamiltonian constraint is removed. We find that some nonmetricity in the connection is allowed, unlike in general relativity. Conditions on the allowable nonmetricity are found. Consideration of the initial value problem confirms that the metric signature should normally be O(3, 2) rather than O(4, 1). Following the lead of earlier works, we argue that concatenation (integration over ) is unnecessary for relating parametrized physics to experience, and propose an alternative to it. Finally, we compare and contrast PGR with other relevant gravitational theories.     

Validity of Parametrized Quark Propagator

Based on an extensively study of the Dyson-Schwinger equations for a fully dressed quark propagator in the “rainbow“ approximation, a parametrized fully dressed quark propagator is proposed in this paper. The parametrized propagator describes a confining quark propagator in hadron since it is analytic everywhere in complex p2-plane and has no Lemmann representation. The validity of the new propagator is discussed by comparing its predictions on selfenergy functions Af(p2), Bf(p2) and effective mass Mf(p2) of quark with flavor f to their corresponding theoretical results produced by Dyson-Schwinger equations. Our comparison shows that the parametrized quark propagator is a good approximation to the fully dressed quark propagator given by the solutions of Dyson-Schwinger equations in the rainbow approximation and is convenient to use in any theoretical calculations.     

Validity of Parametrized Quark Propagator

Based on an extensively study of the Dyson-Schwinger equations for a fully dressed quark propagator in the “rainbow”approximation, a parametrized fully dressed quark propagator is proposed in this paper. The parametrized propagator describes a confining quark propagator in hadron since it is analytic everywhere in complex p2-plane and has no Lemmann representation. The validity of the new propagator is discussed by comparing its predictions on selfenergy functions A/(p2), Bl(p2) and effective mass M$(p2) of quark with flavor f to their corresponding theoretical results produced by Dyson-Schwinger equations. Our comparison shows that the parametrized quark propagator is a good approximation to the fully dressed quark propagator given by the solutions of Dyson-Schwinger equations in the rainbow approximation and is convenient to use in any theoretical calculations.     

Supermulticonformal Field Theory

In this paper we develop the superspacestructure of the multicomplex space MC_n forn = 2ⁿ. We extend the basic properties of themulticomplex analysis to n the case ofSMC_n ^N, called supermulticomplex spaces: this goes from the n superanalyticitycondition to the residue theorem. The formalism of 2Dsuperconformal field theory is also developed onSMC_n ^N. We then show that the nassociated superconformal symmetry is infinite dimensional and leads ton copies of super-Virasoro algebra. This results can beapplied to construct a free-field theory on the volumeof the (n – 1)-super-brane. A model of field theory describing a bosonic case is alsopresented.     

PT-Symmetric Quantum Field Theory

In the context of the PT-symmetric version of quantum electrodynamics, it is argued that the C-operator introduced in order to define a unitary inner product has nothing to do with charge conjugation.     

Shuffling Quantum Field Theory

We discuss shuffle identities between Feynman graphs using the Hopf algebra structure of perturbative quantum field theory. For concrete exposition, we discuss vertex function in massless Yukawa theory.     

Axiomatic Conformal Field Theory

A new rigourous approach to conformal field theory is presented. The basic objects are families of complex-valued amplitudes, which define a meromorphic conformal field theory (or chiral algebra) and which lead naturally to the definition of topological vector spaces, between which vertex operators act as continuous operators. In fact, in order to develop the theory, M?bius invariance rather than full conformal invariance is required but it is shown that every M?bius theory can be extended to a conformal theory by the construction of a Virasoro field. In this approach, a representation of a conformal field theory is naturally defined in terms of a family of amplitudes with appropriate analytic properties. It is shown that these amplitudes can also be derived from a suitable collection of states in the meromorphic theory. Zhu's algebra then appears naturally as the algebra of conditions which states defining highest weight representations must satisfy. The relationship of the representations of Zhu's algebra to the classification of highest weight representations is explained. Received: 22 October 1998 / Accepted: 16 July 1999     

Relative Quantum Field Theory

We highlight the general notion of a relative quantum field theory, which occurs in several contexts. One is in gauge theory based on a compact Lie algebra, rather than a compact Lie group. This is relevant to the maximal superconformal theory in six dimensions.     

Colored Group Field Theory

Random matrix models generalize to Group Field Theories (GFT) whose Feynman graphs are dual to higher dimensional topological spaces. The perturbative development of the usual GFT’s is rather involved combinatorially and plagued by topological singularities (which we discuss in great detail in this paper), thus very difficult to control and unsatisfactory.     

Field Theory on Kappa-spacetime

A general formalism is developed, that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for the -deformed Poincaré algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable -product. Fields are elements of this function algebra. As an example, the Klein-Gordon equation is defined and derived from an action.     

Braided Quantum Field Theory

We develop a general framework for quantum field theory on noncommutative spaces, i.e., spaces with quantum group symmetry. We use the path integral approach to obtain expressions for n-point functions. Perturbation theory leads us to generalised Feynman diagrams which are braided, i.e., they have non-trivial over- and under-crossings. We demonstrate the power of our approach by applying it to φ⁴-theory on the quantum 2-sphere. We find that the basic divergent diagram of the theory is regularised. Received: 3 July 1999 / Accepted: 10 November 2000     

On Field Theory Methods in Singular Perturbation Theory

Singular and supersingular finite rank perturbations of self-adjoint operators are studied using methods from renormalization theory for quantum fields. It is shown that the ideas from dimensional and Pauli–Villars regulatizations can be applied to determine uniquely certain finite rank supersingular perturbations. Approach is based on the regularization of homogeneous singular quadratic forms.     

New Parametrized Entangled State Representations and Their Applications

We construct two new kinds of parametrized entangled states in two-mode Fock space. Using the technique of integration within an ordered product of operators, we prove that they span the complete space. Their applications to solving dynamic problems and finding new generalized squeezing are addressed.     

On Multi-Point Liouville Field Theory

In many cases, the classical or semi-classical Liouville field theory appears in the form of Fuchsian or Riemann differential equations whose solutions cannot be simply found, or atleast require a comprehensive knowledge on analytical techniques of differential equations of mathematical physics. Here, instead of other cumbersome methodologies such as treating with the Heun functions, we use the quasi-exact ansatz approach and thereby solve the so-called resulting two- and three-point differential equations in a very simple manner. We apply the approach to two recent papers in the field.     

Gauge Field Theory for Fermions

Inhomogeneous nonlinear gauge field theory for fermions is studied in detail. We show that the zagrangian of the standard model can be rewritten in terms of the nonlinear connection.     

Relativistic Nonlocal Quantum Field Theory

A theory is defined to be relativistic if its Hamiltonian, total momenta, and boost's generators satisfy commutation relations of the Poincaré group. Field theories with usual local interactions are known to be relativistic. A simple example of a relativistic nonlocal theory is found. However, it has divergences. Some conditions are obtained which are necessary in order that a nonlocal theory be relativistic and divergenceless.     

Interfacial Roughening in Field Theory

In the rough phase, the width of interfaces separating different phases of statistical systems increases logarithmically with the system size. This phenomenon is commonly described in terms of the capillary wave model, which deals with fluctuating, infinitely thin membranes, requiring ad hoc cut-offs in momentum space. We investigate the interface roughening in a unified approach, which does not rely on joining different models, namely in the framework of the Landau-Ginzburg model, that is renormalized field theory, in the one-loop approximation. The interface profile and width are calculated analytically, resulting in finite expressions with definite coefficients. They are valid in the scaling region and depend on the known renormalized coupling constant.