Removing tadpoles in a soliton sector

It has long been known that perturbative calculations can be performed in a soliton sector of a quantum field theory by using a soliton Hamiltonian, which is constructed from the defining Hamiltonian by shifting the field by the classical soliton solution. It is also known that even if tadpoles are eliminated in the vacuum sector, they remain in the soliton sector. In this note we show, in the case of quantum kinks at two loops, that the soliton sector tadpoles may be removed by adding certain quantum corrections to the classical solution used in this construction. Stated differently, the renormalization condition that the soliton sector tadpoles vanish may be satisfied by renormalizing the soliton solution.

NONEQUILIBRIUM THERMO FIELD DYNAMICS FOR RELATIVISTIC COMPLEX SCALAR AND DIRAC FIELDS

Relativistic quantum field theories for complex scalar and Dirac fields are investigated in nonequilibrium thermo field dynamics. The thermal vacuum is defined by the Bogoliubov transformed creation and annihilation operators. Two independent Bogoliubov parameters are introduced for a charged field. Its difference naturally induces the chemical potential. Time-dependent thermal Bogoliubov transformation generates the thermal counterterms. We fix the terms by the self-consistency renormalization condition. Evaluating the thermal self-energy under the self-consistency renormalization condition, we derive the quantum Boltzmann equations for the relativistic fields.

THE ONE-LOOP APPROXIMATION OF THE TRANSITION AMPLITUDE IN KREIN SPACE QUANTIZATION

An explicit calculation of the transition amplitude in the one-loop approximation in Krein space quantization, has been presented in this paper. As we know the loop integrals in the Feynman diagrams will be often diverged, so it is needed to introduce a regulator (Renormalization condition). In Ref. 1 the λϕ4 theory in Krein space has been considered, it has been proved that the disappearance of the ultraviolet divergence to the one-loop approximation is the direct result of Krein space quantization method. Here it is shown that the transition amplitude in the one-loop approximation in Krein space is finite, and its quantity has been calculated. So the theory is automatically regularized.

SUMMING RADIATIVE CORRECTIONS TO THE EFFECTIVE POTENTIAL

When one uses the Coleman–Weinberg renormalization condition, the effective potential V in the massless [Formula: see text] theory with O(N) symmetry is completely determined by the renormalization group functions. It has been shown how the (p + 1) order renormalization group function determine the sum of all the N p LL order contribution to V to all orders in the loop expansion. We discuss here how, in addition to fixing the N p LL contribution to V, the (p + 1) order renormalization group functions can also be used to determine portions of the N p+n LL contributions to V. When these contributions are summed to all orders, the singularity structure of V is altered. An alternate rearrangement of the contributions to V in powers of ln ϕ, when the extremum condition V′(ϕ = v) = 0 is combined with the renormalization group equation, show that either v = 0 or V is independent of ϕ. This conclusion is supported by showing the LL , …, N 4 LL contributions to V become progressively less dependent on ϕ.

REMOVAL OF VIOLATIONS OF THE MASTER WARD IDENTITY IN PERTURBATIVE QFT

We study the appearance of anomalies of the Master Ward Identity, which is a universal renormalization condition in perturbative QFT. The main insight of the present paper is that any violation of the Master Ward Identity can be expressed as a local interacting field; this is a version of the well-known Quantum Action Principle of Lowenstein and Lam. Proceeding in a proper field formalism by induction on the order in ħ, this knowledge about the structure of possible anomalies as well as techniques of algebraic renormalization are used to remove possible anomalies by finite renormalizations. As an example, the method is applied to prove the Ward identities of the O(N) scalar field model.

CONTINUITY OF THE FOUR-POINT FUNCTION OF MASSIVE $\varphi_{4}^{4}$-THEORY ABOVE THRESHOLD

In this paper we prove that the four-point function of massive [Formula: see text]-theory is continuous as a function of its independent external momenta when posing the renormalization condition for the (physical) mass on-shell. The proof is based on integral representations derived inductively from the perturbative flow equations of the renormalization group. It closes a longstanding loophole in rigorous renormalization theory in so far as it shows the feasibility of a physical definition of the renormalized coupling.

WAVE FUNCTION RENORMALIZATION PRESCRIPTION OF UNSTABLE PARTICLE

We define four Wave function Renormalization Constants (WRCs) for unstable particles under the LSZ reduction formula. By CPT conservation law we obtain a new wave function renormalization condition and determine the four WRCs. By calculating the gauge dependence of the physical amplitudes we demonstrate the consistency of the current wave function renormalization prescription with the gauge theory in standard model. We also prove that the conventional wave function renormalization prescription leads to physical amplitudes of gauge dependent.