Schwinger's method for the massive Casimir effect

We apply a method recently proposed by Schwinger to the massive scalar field to calculate the Casimir effect. The method is applied with two different regularization schemes: Schwinger's original one by means of Poisson formula and another one by means of analytical continuation.     

The two-loop renormalization of the gauge coupling and the scalar potential for an arbitrary renormalizable field theory

For any renormalize field theory in four dimensions we obtain the two-loop counterterms for the gauge coupling and the scalar potential, using the background-field method. The calculation was performed in two different subtraction schemes: one is the ordinary dimensional regularization, the other is the so-called dimensional reduction scheme. We show that already at the two-loop level differences occur for the scalar coupling-constants. Only dimensional reduction preserves supersymmetry up to this level.     

压缩算符在自由标量场理论中的推广

引入了一种在量子场论中构造压缩算符的办法:考虑两个具有不同质量的同一标量场的自由哈密顿量,通过博戈留波夫变换,导出广义压缩算符,该算符把一个基态映射到另一个。该算符作用的有效性分别在量子场论的狄拉克表象和薛定谔泛函表象中得到了验证。我们相信,在任意实标量场理论中,只要存在两组以线性变换联系起来的生成湮灭算符,压缩算符就被类似的方法找到。     

Supersymmetrization of scalar field theories

We develop a formalism for constructing the vacuum functional and supersymmetrizing a scalar field theory with the help of its ground state representation. The field theory problem is first transformed into a quantum mechanical one for which the ground state representation is well defined. The theory is then supersymmetrized by “taking the square root” of the hamiltonian. Standard approximation techniques are used to construct the vacuum functional with which spontaneous supersymmetry breaking can be analyzed.     

Conformal supergravity in ten dimensions

We present the complete off-shell structure of conformal supergravity in ten dimensions. It is based on 128 + 128 degrees of freedom and its formulation requires differential constraints. We study how these constraints are resolved in four and five dimensions. Covariant conditions are given that restrict conformal supergravity to its on-shell Poincaré counterpart. In ten dimensions the relationship between the two theories has new and unusual aspects, which we explore in a variety of ways. We rewrite on-shell Poincaré supergravity in a superconformally invariant form, from which we deduce that its off-shell version must contain at least a scalar (chiral) multiplet. We analyze some aspects of the non-linear structure of the field representation based on the conformal fields combined with one scalar multiplet.     

On the Light-Cone Expansion in Gauge Field Theories (QED)

The techniques for the derivation of light-cone expansions in scalar field theories are generalized to nonscalar, especially gauge field theories. For this reason the smallness of the remainder is proved in an arbitrary renormalizable theory provided an infrared regularization is present. Then we apply the formalism to derive a light-cone expansion for the product of two scalar currents in Quantum Electrodynamics in leading order. Thereby the gauge-invariance of the underlying theory is used from the very beginning by the application of the known solutions of the Ward identities. As a result of that, one obtains two gauge-invariant light cone operators, and the corresponding coefficient functions are independent one from another.     

BPHZ renormalization of λφ4 field theory in curved spacetime

A proof is given to all orders in perturbation theory of the renormalizability of λφ⁴ field theory in curved spacetime. The proof is based on the BPHZ definition of a renormalized Feynman integrand and uses dimensional regularization to ensure that products of Feynman propagators are well-defined distributions. The explicit structure of the pole terms in the Feynman integrand is obtained using a local momentum space representation of the Feynman propagator and is shown to be of a form which can be cancelled by counterterms in the scalar field Lagrangian. The proof given is, technically, only valid for metrics which have been analytically continued to Euclidean (++++) signature.     

Variable <Emphasis Type="Italic">G</Emphasis> and <Emphasis Type="Italic">Λ</Emphasis>: scalar-tensor versus RG-improved cosmology

We study the consequences due to time varying G and in scalar-tensor theories of gravity for cosmology, inspired by the modifications introduced by the Renormalization Group (RG) equations in the Quantum Einstein Gravity. We assume a power-law scale factor in presence contemporarily of both the scalar field and the matter components of the cosmic fluid, and analyze a special case and its generalization, also showing the possibility of a phantom cosmology. In both such situations we find a negative kinetic term for the scalar field Q and, possibly, an equation-of-state parameter w _Q < –1. A violation of dominant energy condition (DEC) for Q is also possible in both of them; but, while in the first special case the Q-energy density then remains positive, in the second one we find it negative.This revised version was published online in April 2005. The publishing date was inserted.     

One loop vacuum polarization in a locally de Sitter background

We compute the one loop vacuum polarization from massless, minimally coupled scalar QED in a locally de Sitter background. Gauge invariance is maintained through the use of dimensional regularization, whereas conformal invariance is explicitly broken by the scalar kinetic term as well as through the conformal anomaly. A fully renormalized result is obtained. The one loop corrections to the linearized, effective field equations do not vanish when evaluated on-shell. In fact the on-shell one loop correction depends quadratically on the inflationary scale factor, similar to a photon mass. The contribution from the conformal anomaly is insignificant by comparison.     

Polyakov effective action from functional renormalization group equation

We discuss the Polyakov effective action for a minimally coupled scalar field on a two dimensional curved space by considering a non-local covariant truncation of the effective average action. We derive the flow equation for the form factor in , and we show how the standard result is obtained when we integrate the flow from the ultraviolet to the infrared.     

Renormalized energy-momentum tensor of λ Φ<Superscript>4</Superscript> theory in curved space-time

Divergenceless expression for the energy-momentum tensor of scalar field is obtained using the momentum cut-off regularization technique. We consider a scalar field with quartic self-coupling in a spatially flat (3+1)-dimensional Robertson-Walker space-time, having arbitrary mass and coupled to gravity. As special cases, energy-momentum tensor for conformal and minimal coupling are also obtained. The energy-momentum tensor is observed to exhibit trace anomaly in curved space-time     

Infrared regularization of the massless scalar free field in two-dimensional space-time via Lorentz expansion

It is shown that Lorentz harmonics provide a natural basis for the expansion and infrared regularization of a massless scalar field in two dimensions. The negative metric operators separate out simply. Each Lorentz component of the field is partially local.     

Integral quantizations with two basic examples

The paper concerns integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also insist on the inherent probabilistic aspects of this classical–quantum map. The approach includes and generalizes coherent state quantization. Two applications based on group representation are carried out. The first one concerns the Weyl–Heisenberg group and the euclidean plane viewed as the corresponding phase space. We show that a world of quantizations exist, which yield the canonical commutation rule and the usual quantum spectrum of the harmonic oscillator. The second one concerns the affine group of the real line and gives rise to an interesting regularization of the dilation origin in the half-plane viewed as the corresponding phase space.     

Technique for interaction of optical fields with turbulent medium containing particles

We develop a method for transmission of stochastic fields through turbulent media (atmosphere, ocean, biotissues) containing randomly distributed particles. The method is based on the angular spectrum representation of stochastic, statistically stationary, scalar fields, the Rytov perturbation series for propagation in weakly fluctuating media, and the first Born approximation for weak scattering from particulate media. The results for transmission of the deterministic (laser) field may be obtained from our general results as a limiting case.     

Casimir effect for a scalar field via Krein quantization

In this work, we present a rather simple method to study the Casimir effect on a spherical shell for a massless scalar field with Dirichlet boundary condition by applying the indefinite metric field (Krein) quantization technique. In this technique, the field operators are constructed from both negative and positive norm states. Having understood that negative norm states are un-physical, they are only used as a mathematical tool for renormalizing the theory and then one can get rid of them by imposing some proper physical conditions.     

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.     

Gauge invariant regularization of Yang-Mills wave functionals

We present a gauge invariant nonperturbative regularization of gauge theories in the temporal gauge. We use the Schrödinger representation for field theory. An example is given to illustrate regularization using wave functionals.     

Two regularization types as two different Nambu-Iona-Lasinio models

The Nambu-Iona-Lasinio models with 4-dimensional cutting and dimensional-analytical regularization types are compared. It is demonstrated that they describe two different models of light quark interaction. In the average-field approximation, the behavior of the scalar amplitude differs in the threshold region. Unlike the 4-dimensional cutting regularization in which the pole term corresponding to a sigma-meson can be separated near the threshold, the singularity of the scalar amplitude in the dimensional-analytical regularization is non-pole; moreover, it disappears completely for a certain value of the regularization parameter. One more significant difference between the two models is in the first-order expansion of the average field. The calculated meson contributions to the quark chiral condensate and dynamic quark mass demonstrate that despite their relative smallness, they can destabilize the Nambu-Iona-Lasinio model with 4-dimensional cutting regularization. On the contrary, the model with dimensional-analytical regularization is stabilized, which is manifested through a shift of regularization parameter values toward the stability region in which the contributions themselves decrease. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 20–31, April, 2006.