Related papers: Numerical evaluation of a two loop diagram in the …
The two loop effective potential of massless $\lambda\phi^4$ theory was presented in several regularization and renormalization prescriptions and the dynamical symmetry breaking solution was obtained in strong coupling situation in several…
We illustrated via the sunset diagram that dimensional regularization 'deforms' the nonlocal contents of multi-loop diagrams with its equivalence to cut-off regularization scheme recovered only after sub-divergence were subtracted. Then we…
We consider the most general loop integral that appears in non-relativistic effective field theories with no light particles. The divergences of this integral are in correspondence with simple poles in the space of complex space-time…
Through two loop effective potential we demonstrate that the $\bar{MS}$ scheme of dimensional regularization and Jackiw's prescription in cut-off regularization allow for the dynamical breaking solution in massless $\lambda\phi^4$ theory,…
Explicit two-loop calculations in noncommutative $\phi^4_4$ theory are presented. It is shown that the model is two-loop renormalizable.
Abandoning dimensional regularization allows important simplifications in loop calculations and gives a handle to interpret non-renormalizable Quantum Field Theories. I review the current status of FDR, a fully four-dimensional approach to…
We propose an implicit regularisation scheme. The main advantage is that since no explicit use of a regulator is made, one can in principle avoid undesirable symmetry violations related to its choice. The divergent amplitudes are split into…
We consider two loop sunset diagrams with two mass scales m and M at the threshold and pseudotreshold that cannot be treated by earlier published formula. The complete reduction to master integrals is given. The master integrals are…
This paper discusses the methods and the results used in an accompanying paper describing the matching of effective chiral Lagrangians in dimensional and lattice regularizations. We present methods to compute 2-loop massless sunset diagrams…
By use of the threshold expansion we develop an algorithm for analytical evaluation, within dimensional regularization, of arbitrary terms in the expansion of the (two-loop) sunset diagram with general masses m_1, m_2 and m_3 near its…
A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…
The tensor renormalization group attracts great attention as a new numerical method that is free of the sign problem. In addition to this striking feature, it also has an attractive aspect as a coarse-graining of space-time; the…
We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, renormalization scheme dependence of the scattering amplitude can only…
We investigate (1+1)-dimensional $\phi^4$ field theory in the symmetric and broken phases using discrete light-front quantization. We calculate the perturbative solution of the zero-mode constraint equation for both the symmetric and broken…
The role of cut-off and dimensional regularizations is discussed in the context of obtaining a renormalized nucleon-nucleon potential from the chiral Lagrangian formulation of the effective field theory due to Weinberg. Both types of…
The renormalization of effective potential for the noncommutative scalar field theory is investigated to the two-loop approximation. It is seen that the nonplanar diagram does not appear in the one-loop potential. However, nonplanar diagram…
Explicit divergences and counterterms do not appear in the differential renormalization method, but they are concealed in the neglected surface terms in the formal partial integration procedure used. A systematic real space cutoff procedure…
We study cutoff and lattice effects in the O(n) symmetric $\phi^4$ theory for a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions. In the large-N limit above $T_c$, we show that $\phi^4$ field theory at finite…
We make a detailed analysis of the spontaneous $Z_{2}$-symmetry breaking in the two dimensional real $\phi^{4}$ theory with the tensor renormalization group approach, which allows us to take the thermodynamic limit easily and determine the…
The structure of loop corrections is examined in a scalar field theory on a three dimensional space whose spatial coordinates are noncommutative and satisfy SU(2) Lie algebra. In particular, the 2- and 4-point functions in $\phi^4$ scalar…