Renormalization of massless fields with hard-soft infrared decomposition

The decomposition of Feynman integrals with massless propagators into hard and soft contributions is systematically effected in renormalized field theory. It is shown that the decomposition leads to an elegant method of renormalizing massless field theories. Ultraviolet and infrared finite composite fields (normal products) are defined and renormalized field equations are derived. Exploiting a gauge principle, scalar ghosts arising in the hard-soft decomposition are eliminated and a renormalization group equation is derived to describe the effects of changes in the mass scale.     

Two-Point Function Reduction of Four-Point Amputated Functions and Transformations in FF and RA Basis in a Real-Time Finite Temperature NJL Model

Based on a general analysis of Green functions in the real-time thermal field theory, we have proven that the four-point amputated functions in an NJL model in the fermion bubble diagram approximation behave like usual two-point functions. We expound the thermal transformations of the matrix propagators for a scalar bound state in the FF basis and in the RA basis respectively. The resulting physical causal, advanced and retarded propagators are respectively identical to corresponding ones derived in the imaginary-time formalism, and this shows once again the complete equivalence of the two formalisms of thermal field theory on the discussed problem in the NJL model.     

Study of a two-dimensional model with axial-current-pseudoscalar derivative interaction

A detailed study is made of a massive pseudoscalar field interacting via derivative coupling with massless fermions in two-dimensional space-time. The model provides an example of a soluble renormalizable theory with an anomalous axial-vector current and a zero-mass particle interpretation for the fermion. Except for a finite mass and wavefunction renormalization, the boson remains free in the presence of the interaction. The canonical fermion field exhibits an anomalous dimension that is found to be in agreement with the asymptotic Callan-Symanzik equation. The connection between the Wilson expansion for defining operator products in this model and the Dyson equations of renormalized perturbation theory is discussed, and agreement with second-order perturbation theory is verified by explicit calculation.     

The two-loop renormalization of the Yukawa sector for an arbitrary renormalizable field theory

The two-loop Yukawa coupling constant renormalization and the mass renormalization of the fermion for an arbitrary renormalizable field theory, including vector, scalar and of course fermion fields, has been calculated. This has been done in two different regularization schemes, i.e. dimensional regularization and dimensional reduction. Both calculations were done in the conventional way, and not with the use of the so-called background-field method. Only the reduction scheme is shown to preserve supersymmetry up to this level.Furthermore a simple example of a gauge theory is given to show that in general it is not possible to give an explicit transformation of the coupling constants in such a way that all β-functions become the same for the two regularization schemes, which proves that dimensional reduction, treated this way, is not a good regularization scheme.     

Two-point fermion correlation functions at finite density

The general form of two-point fermion correlation functions at finite density is examined. Examples of particular interest are correlation functions of nucleonic interpolating fields, used in QCD sum-rule studies, and nucleon propagators in hadronic field theories. The constraints of Lorentz covariance, parity, and time-reversal on the form of the correlators are derived by focusing on spectral functions. Discrepancies with other treatments in the literature are discussed.     

Consistent real-time propagators for any spin,mass, temperature and density

The time-path method in finite temperature field theory is extended to arbitrary covariant fields. Explicit expressions for the free thermal propagators are obtained using the multi-mass Klein-Gordon divisor. The key formula which shows that the interacting theory is free of singularities is derived. Finally, a simple method for the determination of free massless propagators is given.     

Heavy fermion quantum criticality

During the last few years, investigations of rare-earth materials have made clear that heavy fermion quantum criticality exhibits novel physics not fully understood. In this work, we write for the first time the effective action describing the low energy physics of the system. The f fermions are replaced by a dynamical scalar field whose nonzero expected value corresponds to the heavy fermion phase. The effective theory is amenable to numerical studies as it is bosonic, circumventing the fermion sign problem. Via effective action techniques, renormalization group studies, and Callan-Symanzik resummations, we describe the heavy fermion criticality and predict the heavy fermion critical dynamical susceptibility and critical specific heat. The specific heat coefficient exponent we obtain (0.39) is in excellent agreement with the experimental result at low temperatures (0.4).     

A Lie algebraic approach to the Kondo problem

The Kondo problem is approached using the unitary Lie algebra of spin-singlet fermion bilinears. In the limit when the number of values of the spin N goes to infinity the theory approaches a classical limit, which still requires a renormalization. We determine the ground state of this renormalized theory. Then we construct a quantum theory around this classical limit, which amounts to recovering the case of finite N.     

New quantization conditions for field theory without divergence

Quantum field theory is a fundamental tool in particle and nuclear physics. Elemental particles are assumed to be point particles and, as a result, the loop integrals are divergent in many cases. Regularization and renormalization are introduced in order to get the physical finite results from the infinite, divergent loop integrations. We propose new quantization conditions for the fields whose base is very natural, i.e., any particle is not a point particle but a solid one with three dimensions. With this solid quantization, divergence could disappear.     

Infrared problems in quantum electrodynamics

We present a self-contained treatment of the infrared problem in Quantum Electrodynamics. Our program includes a derivation and proof of finiteness of modified reduction formulae for scattering in Coulomb potentials and unitary extensions of the relativistic Coulomb amplitudes in the forward direction. The renormalization structure of the theory is discussed in connection with the infrared problem and the renormalization group is reconsidered and shown to be inadequate for the “improvement” of perturbation theoretic results. However, simple forms of the renormalization group equations are easily established, which allow for a simple discussion of the renormalization structure and the extraction of physical quantities out of Green functions normalized at an arbitrary mass μ < m (m is the fermion mass). As an example of such a quantity we consider the construction of a renormalized and infrared finite mass-operator in presence of external fields. Scattering theory in Quantum Electrodynamics is elaborated in the context of the coherent state formulation of the asymptotic condition. Dimensional regularization techniques are systematically used for the reduction of coherent states and the construction of S-matrix elements and the cross-section formulae. The latter are obtained in a relatively simple form, which allows for a direct comparison with the exact cross-section formulae derived in the traditional context. This establishes the equivalence of the two approaches at the cross-section level. Various applications illustrate the techniques presented here and relative topics are discussed.     

Effective potential in curved space and cut-off regularizations

We consider derivation of the effective potential for a scalar field in curved space-time within the physical regularization scheme, using two sorts of covariant cut-off regularizations. The first one is based on the local momentum representation and Riemann normal coordinates and the second is operatorial regularization, based on the Fock-Schwinger-DeWitt proper-time representation. We show, on the example of a self-interacting scalar field, that these two methods produce equal results for divergences, but the first one gives more detailed information about the finite part. Furthermore, we calculate the contribution from a massive fermion loop and discuss renormalization group equations and their interpretation for the multi-mass theories.     

Equations from non-linear chiral transformations

In comparison with theWT chiral identity which is indispensable for renormalization theory, relations deduced from the non-linear chiral transformation have a totally different physical significance. We wish to show that non-linear chiral transformations are powerful tools to deduce useful integral equations for propagators. In contrast to the case of linear chiral transformations, identities derived from non-linear ones contain more involved radiative effects and are rich in physical content. To demonstrate this fact we apply the simplest non-linear chiral transformation to the Nambu-Jona-Lasinio model, and show how our identity is related to the Dyson-Schwinger equation and Bethe-Salpeter amplitudes of the Higgs and π. Unlike equations obtained from the effective potential, our resultant equation is exact and can be used for events beyond the LEP energy.     

Spontaneous breakdown and finiteness of supersymmetric theories in two dimensions

Using a single scalar superfield we construct the two dimensional version of the four dimensional Wess-Zumino model and examine its renormalization properties. In the context of this model and in the tree approximation we find that supersymmetry can be spontaneously broken with the appearance of a massless fermion. This solution is then shown to be dynamically unstable at the one-loop level. Finally we use supersymmetry to construct two dimensional theories for which all IPI vertices are finite.     

Geometric Origin of Physical Constants in a Kaluza-Klein Tetrad Model

An important feature of Kaluza-Klein theories is their ability to relate fundamental physical constants to the radii of higher dimensions. In previous Kaluza-Klein theory, which unifies the electromagnetic field with gravity as dimensionless components of a Kaluza-Klein metric, i) all fields have the same physical dimensions, ii) the Lagrangian has no explicit dependence on any physical constants except mass, and hence iii) all physical constants in the field equations except for mass originate from geometry. While it seems natural in Kaluza-Klein theory to add fermion fields by defining higher-dimensional bispinor fields on the Kaluza-Klein manifold, these Kaluza-Klein theories do not satisfy conditions (i), (ii), and (iii). In this paper, we show how conditions (i), (ii), and (iii) can be satisfied by including bispinor fields in a tetrad formulation of the Kaluza-Klein model, as well as in an equivalent teleparallel model. This demonstrates an unexpected feature of Dirac's bispinor equation, since conditions (i), (ii), (iii) imply a special relation among the terms in the Kaluza-Klein or teleparallel Lagrangian that would not be satisfied in general.     

New quantization conditions for field theory without divergence

Quantum field theory is a fundamental tool in particle and nuclear physics. Elemental particles are assumed to be point particles and, as a result, the loop integrals are divergent in many cases. Regularization and renormalization are introduced in order to get the physical finite results from the infinite, divergent loop integrations. We propose new quantization conditions for the fields whose base is very natural, i.e., any particle is not a point particle but a solid one with three dimensions. With this solid quantization, divergence could disappear.     

Finite BRST Mapping in Higher-Derivative Models

We continue the study of finite field-dependent BRST (FFBRST) symmetry in the quantum theory of gauge fields. An expression for the Jacobian of path integral measure is presented, depending on a finite field-dependent parameter, and the FFBRST symmetry is then applied to a number of well-established quantum gauge theories in a form which incudes higher-derivative terms. Specifically, we examine the corresponding versions of the Maxwell theory, non-Abelian vector field theory, and gravitation theory. We present a systematic mapping between different forms of gauge-fixing, including those with higher-derivative terms, for which these theories have better renormalization properties. In doing so, we also provide the independence of the S-matrix from a particular gauge-fixing with higher derivatives. Following this method, a higher-derivative quantum action can be constructed for any gauge theory in the FFBRST framework.     

Heavy-particle-induced effective lagrangian in spontaneously broken theories (II). The abelian Higgs-Kibble model

In the context of the abelian Higgs-Kibble model with a charged fermion, we study in detail low-energy effective field theories of light particles when the heavy mass scales in the theory are generated by the Higgs-Kibble mechanism. Our analysis is based on the systematic use of factorization methods, and is valid to all orders in renormalized perturbation theory. Emphasis is given to finding the vestiges of the original (spontaneously broken) local gauge symmetry left in low-energy effective field theories, and general techniques are developed for that purpose. When only Fermi fields or / and physical Higgs fields correspond to light particles, low-energy effective field theories do not exhibit such signs. On the other hand, when physical gauge fields (together with other unphysical fields) correspond to light particles, the original local gauge symmetry restricts the resulting low-energy effective local action to a non-trivial form.     

Critical dynamics of superconductors in the charged regime

We investigate the finite temperature critical dynamics of three-dimensional superconductors in the charged regime, described by a transverse gauge field coupling to the superconducting order parameter. Assuming relaxational dynamics for both the order parameter and the gauge fields, within a dynamical renormalization group scheme, we find a new dynamic universality class characterized by a finite fixed point ratio between the transport coefficients associated with the order parameter and gauge fields, respectively. We find signatures of this universality class in various measurable physical quantities, and in the existence of a universal amplitude ratio formed by a combination of physical quantities.     

Fermion propagators on a four-dimensional random-block lattice

Fermion propagators, composite boson propagators and the fermion condensate are calculated numerically on the four-dimensional random-block lattice, respectively. The ensemble-averaged fermion propagator agrees with the continuum propagator for distances greater than three average lattice spacings. The results on the fermion condensate show that the chiral symmetry of the doubled modes is broken in the continuum limit. The Goldstone boson arising from the broken symmetry is revealed by examining the composite pseudo-scalar propagator. The doubled fermion and the Goldstone boson both acquire masses of the order of inverse lattice spacing and thus decouple from the theory in the continuum limit.     

Inertial Mass and Vacuum Fluctuations in Quantum Field Theory

Motivated by recent works on the origin of inertial mass, we revisit the relationship between the mass of charged particles and zero-point electromagnetic fields. To this end we first introduce a simple model comprising a scalar field coupled to stochastic or thermal electromagnetic fields. Then we check if it is possible to start from a zero bare mass in the renormalization process and express the finite physical mass in terms of a cut-off. In scalar QED this is indeed possible, except for the problem that all conceivable cut-offs correspond to very large masses. For spin-1/2 particles (QED with fermions) the relation between bare mass and renormalized mass is compatible with the observed electron mass and with a finite cut-off, but only if the bare mass is not zero; for any value of the cut-off the radiative correction is very small.