Symanzik–Becchi–Rouet–Stora lessons on renormalizable models with broken symmetry: The case of Lorentz violation (original) (raw)
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Nuclear and Particle Physics Proceedings, 2015
We study the possible effects of large Lorentz violations that can appear in the effective models in which the Lorentz symmetry breakdown is performed with higher-order operators. For this we consider the Myers and Pospelov extension of QED with dimension-five operators in the photon sector and standard fermions. We focus on the fermion self-energy at one-loop order and find small and finite radiative corrections in the even CPT sector. In the odd CPT sector a lower dimensional operator is generated which contains unsuppressed effects of Lorentz violation leading to a possible fine-tuning. For the calculation of divergent diagrams we use dimensional regularization and consider an arbitrary background four-vector.
Renormalization scheme dependence of \beta -functions in Lorentz-violating quantum field theory
The European Physical Journal C
Effective quantum field theories that allow for the possibility of Lorentz symmetry violation can sometimes also include redundancies of description in their Lagrangians. Explicit calculations in a Lorentz-violating generalization of Yukawa theory show that when this kind of redundancy exists, different renormalization schemes may lead to different expressions for the renormalization group \beta β -functions, even at only one-loop order. However, the renormalization group scaling of physically observable quantities appears not to share this kind of scheme dependence.
Renormalization group approach for Lorentz-violating scalar field theory at all loop orders
International Journal of Geometric Methods in Modern Physics, 2016
We compute, both explicitly, at least, up to next-to-leading order and in a proof by induction for all loop levels, the critical exponents for thermal Lorentz-violating O([Formula: see text]) self-interacting scalar field theory. They are evaluated in a massless theory renormalized at arbitrary external momenta, where a reduced number of Feynman diagrams is needed. The results are presented and shown to be identical to that found previously in distinct theories renormalized at different renormalization schemes. Finally, we give both mathematical explanation and physical interpretation for them based on coordinates redefinition techniques and symmetry ideas, respectively.
Renormalization Of High-Energy Lorentz Violating Four Fermion Models
2010
We study the one-loop renormalization of high-energy Lorentz violating four fermion models. We derive general formulas and then consider a number of specific models. We study the conditions for asymptotic freedom and give a practical method to determine the asymptotic-freedom domain. We also point out that in some models the RG flow contains "rational" Zimmermann trajectories that might hide new symmetries.
Dynamical Lorentz Symmetry Breaking from 3+ 1 Renormalizable Model with Wess-Zumino Interaction
1996
We study the renormalizable abelian vector-field models in the presence of the Wess-Zumino interaction with the pseudoscalar matter. The renormalizability is achieved by supplementing the standard kinetic term of vector fields with higher derivatives. The appearance of fourth power of momentum in the vector-field propagator leads to the super-renormalizable theory in which the β-function, the vector-field renormalization constant and the anomalous mass dimension are calculated exactly. It is shown that this model has the infrared stable fixed point and its low-energy limit is non-trivial. The modified effective potential for the pseudoscalar matter leads to the occurrence of the quantum dynamical breaking of Lorentz symmetry.
Dilatation invariance and spontaneous symmetry breakdown in dimensional renormalization
Nuclear Physics B, 1986
paper completes a sy,,,tematic study of the renormalization of scale invariant models ~ith spontaneotl.', symmetry breakdown discu~,,,in~, an effective scheme for the con,,,truction of Fevnm,m amplitude,',. From a general point of view the original scale invariance of the m~xtclx is accounted for by constraining the dilatation anomalie,,, with a minimality criterion anab, zcd in a prcviou.', paper. This criterion is ha.,,cd on a k~'al Ward identity where the anomalie~ appear ~ouplcd to a ~,purion field. I lore the general framework is adapted to ;. dimcn~,ional renormalizalion ,.chcm¢ ;.rod it is shown to bc equivalent to a scale invariant choice of all cokmlertcrlll.'i and. a~, it h;.tppcns ira minimal scheme.,,, to the mass independence of the rcnormaliz:~tion con,,,tant.~, Ihcrcbv allowing a derivation of a rcnormalization ~,rt~llp equation with standard (mar,~. independent) ct,cfl'icicnt.,.. The whole analy~.i~ rcfcr.s a~. an example to the .,,implc~,t bosonic tn~,.Icl ~.'~mtainin~ all the fcalttrcs conllnon tt~ SCZlIc invariant theories with xpontitncotts .,.vnnuctry brcakdt~wn.
Extending the Standard Model to Include CPT and Lorentz-Breaking Terms
1999
Low-energy remnant fundamental symmetry violations may be present in nature at levels attainable in upcoming experiments. These effects may arise through spontaneous symmetry breaking in a more complete Lorentz covariant theory underlying the standard model. In this work the issue of parameterizing such violations in a consistent and complete manner is addressed. The approach is to use the mechanism of spontaneous symmetry breaking to generate all possible terms consistent with gauge invariance and power-counting renormalizability to construct an extension of the standard model that includes Lorentz- and CPT-breaking terms. A consistent quantization of the theory is developed, conventional quantum field theoretic techniques are shown to apply, and some ramifications for quantum electrodynamics are explored.
Asymptotic states and renormalization in Lorentz-violating quantum field theory
Physical Review D, 2014
Asymptotic single-particle states in quantum field theories with small departures from Lorentz symmetry are investigated. To this end, one-loop radiative corrections for a sample Lorentz-violating Lagrangian contained in the Standard-Model Extension (SME) are studied. It is found that the spinor kinetic operator is modified in momentum space by Lorentz-violating operators not present in the original Lagrangian. It is demonstrated how both the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism need to be adapted as a consequence of this result.
Lorentz-violating extension of the standard model
Physical Review D, 1998
; accepted for publication in Phys. Rev. D) In the context of conventional quantum field theory, we present a general Lorentz-violating extension of the minimal SU(3) × SU(2)× U(1) standard model including CPT-even and CPTodd terms. It can be viewed as the low-energy limit of a physically relevant fundamental theory with Lorentz-covariant dynamics in which spontaneous Lorentz violation occurs. The extension has gauge invariance, energy-momentum conservation, and covariance under observer rotations and boosts, while covariance under particle rotations and boosts is broken. The quantized theory is hermitian and power-counting renormalizable, and other desirable features such as microcausality, positivity of the energy, and the usual anomaly cancellation are expected. Spontaneous symmetry breaking to the electromagnetic U(1) is maintained, although the Higgs expectation is shifted by a small amount relative to its usual value and the Z 0 field acquires a small expectation. A general Lorentz-breaking extension of quantum electrodynamics is extracted from the theory, and some experimental tests are considered. In particular, we study modifications to photon behavior. One possible effect is vacuum birefringence, which could be bounded from cosmological observations by experiments using existing techniques. Radiative corrections to the photon propagator are examined. They are compatible with spontaneous Lorentz and CPT violation in the fermion sector at levels suggested by Planck-scale physics and accessible to other terrestrial laboratory experiments.
On the Renormalizability of Theories With Gauge Anomalies
International Journal of Modern Physics A, 2000
We consider the detailed renormalization of two (1+1)-dimensional gauge theories which are quantized without preserving gauge invariance: the chiral and the "anomalous" Schwinger models. By regularizing the non-perturbative divergences that appear in fermionic Green's functions of both models, we show that the "tree level" photon propagator is illdefined, thus forcing one to use the complete photon propagator in the loop expansion of these functions. We perform the renormalization of these divergences in both models to one loop level, defining it in a consistent and semi-perturbative sense that we propose in this paper.