On the renormalization of the complex scalar free field theory

Ferrari, R.

doi:10.1063/1.3337687

Cited by 9 publications

(9 citation statements)

References 38 publications

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“…While in the nonlinear case the situation is fuzzier. In recent works [21,22,23,24,25,26,27,28,29,30,31,32], we proposed a divergences subtraction scheme for the nonlinear sigma model for the massive Yang-Mills theory and for the Electroweak Model SU(2) ⊗ U(1). Locality and perturbative unitarity are obeyed.…”

Section: Introductionmentioning

confidence: 99%

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Ferrari¹

2012

Acta Phys. Pol. B

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In the present paper, we study the limit of zero mass in non-Abelian gauge theories both with Higgs mechanism and in the nonlinear realization of the gauge group (Stückelberg mass). We argue that in the first case the longitudinal modes undergo a metamorphosis process to the Goldstone scalar modes, while in the second, we guess, a decoupling process associated to a phase transformation. The two scenarios yield strikingly different behaviors at high energy, mainly ascribed to the presence of a massless Higgs doublet among the physical modes in the case of Higgs mechanism (i.e. not only the Higgs boson). The aim of this work is to show that the problem of unitarity at high energy in non-Abelian gauge theory with no Higgs boson can open new perspectives in quantum field theory. 1 After the work of J.M. Cornwall, D.N. Levin, G. Tiktopoulos, M.S. Chanowitz and M.K. Gaillard, the relation between the S-matrix elements for longitudinal modes of the gauge fields and those of the Goldstone bosons has developed to a somewhat more complex result than the one implied by the theorem on the point transformations of fields in scattering theory [17]. The present work adds more consequences to the discovery of the above mentioned physicists. Thus, we choose to denote the theorem by their names.

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Section: Introductionmentioning

confidence: 99%

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Ferrari¹

2012

Acta Phys. Pol. B

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“…This subtraction procedure has been implemented in the one-loop calculation of the gauge field two-point functions [15], [18]. Moreover, it has been tested for a solvable model [19].…”

Section: Subtraction Proceduresmentioning

confidence: 99%

Of higgs, unitarity and other questions

Bettinelli

Ferrari

Quadri

2011

Proc. Steklov Inst. Math.

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On the verge of conclusive checks on the Standard Model by the LHC, we discuss some of the basic assumptions. The reason for this analysis stems from a recent proposal of an Electroweak Model based on a nonlinearly realized gauge group SU (2) ⊗ U (1), where, in the perturbative approximation, there is no Higgs boson. The model enjoys the Slavnov-Taylor identities and therefore the perturbative unitarity. On the other hand, it is commonly believed that the existence of the Higgs boson is entangled with the property of unitarity, when high energy processes are considered. The argument is based mostly on the Froissart bound and on the Equivalence Theorem. In this talk we briefly review some of our objections on the validity of such arguments. Some open questions are pointed out, in particular on the limit of zero mass for the vector mesons and on the fate of the longitudinal polarizations.

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“…The massive NLSM in the LFE formulation has been studied in [15], while the symmetric subtraction procedure for the LFE associated with polar coordinates in the simplest case of the free complex scalar field has been given in [16].…”

Section: Cohomological Analysis Of the Lfementioning

confidence: 99%

“…The results reviewed here are based mainly on References [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach

Quadri

2014

Symmetry

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We summarize recent progress on the symmetric subtraction of the Non-Linear Sigma Model in D dimensions, based on the validity of a certain Local Functional Equation (LFE) encoding the invariance of the SU(2) Haar measure under local left transformations. The deformation of the classical non-linearly realized symmetry at the quantum level is analyzed by cohomological tools. It is shown that all the divergences of the one-particle irreducible (1-PI) amplitudes (both on-shell and off-shell) can be classified according to the solutions of the LFE. Applications to the non-linearly realized Yang-Mills theory and to the electroweak theory, which is directly relevant to the model-independent analysis of LHC data, are briefly addressed.

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On the renormalization of the complex scalar free field theory

Abstract: Polar coordinates are used for the complex scalar free field in D = 4 dimensions. The resulting non renormalizable theory is healed by using a recently proposed symmetric subtraction procedure. The existence of the coordinates transformation is proved by construction.

Cited by 9 publications

References 38 publications

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Of higgs, unitarity and other questions

Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach

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