Related papers: Naturalness and Renormalization Group in the Stand…
The notion of a homogeneous standard filtration of $\sigma$-algebras was introduced by the author in 1970. The main theorem asserted that a homogeneous filtration is standard, i.e., generated by a sequence of independent random variables,…
We develop a technique for normalization for $\infty$-type theories. The normalization property helps us to prove a coherence theorem: the initial model of a given $\infty$-type theory is $0$-truncated. The coherence theorem justifies…
A concept of "guessability" is defined for sets of sequences of naturals. Eventually, these sets are thoroughly characterized. To do this, a nonstandard logic is developed, a logic containing symbols for the ellipsis as well as for…
We derive the Gell-Mann and Low renormalization group equation in the Wilsonian approach to renormalization of massless $g\phi^4$ in four dimensions, as a particular case of a non-linear equation satisfied at any scale by the Wilsonian…
We reconsider the choice of renormalization schemes in a differential-equation approach to aid the discussion of the renormalization of the unstable particles and the CKM matrix in the Standard Model. Certain mass dependent schemes do not…
We define a finite size renormalization scheme for $\phi^4$ theory which in the thermodynamic limit reduces to the standard scheme used in the broken phase. We use it to re-investigate the question of triviality for the four dimensional…
We give criteria for certain morphisms from an algebraic stack to a (not necessarily algebraic) stack to admit an (appropriately defined) scheme-theoretic image. We apply our criteria to show that certain natural moduli stacks of local…
The hierarchy problem in the Standard Model is usually understood as both a technical problem of stability of the calculation of the quantum corrections to the masses of the Higgs sector and of the unnatural difference between the Planck…
We outline the renormalization of the standard model to all orders of perturbation theory in a way which does not make essential use of a specific subtraction scheme but is based on the Slavnov-Taylor identity. Physical fields and…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
Causal perturbative renormalization within the recursive Epstein-Glaser scheme involves extending, at each order, time-ordered operator-valued distributions to coinciding points. This is achieved by a generalized Taylor subtraction on test…
Using the renormalization group techniques it was previously shown that the perturbative effective potential in the $\mathcal{O}(N)$ symmetric $\phi^4$ theory, massless scalar electrodynamics as well as in the conformal limit of the…
We aim here to show that reductionism and emergence play a complementary role in understanding natural processes and in the dynamics of science explanation. In particular, we will show that the renormalization group - one of the most…
The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of $\sigma$-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras. One of the key notions, that of…
We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.
Renormalization group (RG) and resummation techniques have been used in $N$-component $\phi^4$ theories at fixed dimensions below four to determine the presence of non-trivial IR fixed points and to compute the associated critical…
The general prescription for constructing the continuum limit of a field theory is explained using Wilson's renormalization group. We then formulate the renormalization group in perturbation theory and apply it to the four dimensional phi4…
The quadratically divergent scalar mass is subtractively renormalized unlike other divergences which are multiplicatively renormalized. We re-examine some technical aspects of the subtractive renormalization, in particular, the mass…
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining…
We present a radically new proposal for the solution of the naturalness/hierarchy problem, where the fine-tuning of the Higgs mass finds its physical explanation and the well-known multiplicative renormalization of the usual perturbative…