Dimensional regularization of nonlinear sigma models on a finite time interval

Bastianelli, Fiorenzo; Corradini, Olindo; Nieuwenhuizen, P. van

doi:10.1016/s0370-2693(00)01180-1

Cited by 28 publications

(61 citation statements)

References 20 publications

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“…We have used the recently developed dimensional regularization scheme for quantum mechanical path integrals [10] to compute the trace anomaly for a scalar field in six dimensions. The identification of the full anomaly required a complete 4-loop quantum mechanical computation.…”

Section: Discussionmentioning

confidence: 99%

“…In mode regularization and time slicing such counterterms are noncovariant. In the DR scheme the counterterm is covariant and equal to V DR = R 8 , as demonstrated in [10,11]. Now, let us describe the DR scheme which we are going to apply in the next section.…”

Section: Dimensional Regularization Of the Path Integralmentioning

confidence: 99%

“…Recently, following the suggestion in ref. [9] of using dimensional regularization a third way of properly defining the path integrals has been developed in [10]: the dimensional regularization scheme (DR). While the counterterms required in MR and TS are noncovariant, they happen to be covariant in the DR scheme [10,11,9].…”

Section: Introductionmentioning

confidence: 99%

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6D trace anomalies from quantum mechanical path integrals

Bastianelli

Corradini

2001

Phys. Rev. D

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We use the recently developed dimensional regularization (DR) scheme for quantum mechanical path integrals in curved space and with a finite time interval to compute the trace anomalies for a scalar field in six dimensions. This application provides a further test of the DR method applied to quantum mechanics. It shows the efficiency in higher loop computations of having to deal with covariant counterterms only, as required by the DR scheme.

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Section: Discussionmentioning

confidence: 99%

Section: Dimensional Regularization Of the Path Integralmentioning

confidence: 99%

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6D trace anomalies from quantum mechanical path integrals

Bastianelli

Corradini

2001

Phys. Rev. D

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“…The nonlinearities present in the kinetic term make the definition of the path integral rather subtle, carrying the necessity of specifying a regularization scheme together with the fixing of corresponding finite counterterms. The latter are needed for specifying a well-defined quantum theory; see [2][3][4][5] for the known regularization schemes. The development of those regularization schemes was prompted by the a e-mail: fiorenzo.bastianelli@bo.infn.it b e-mail: olindo.corradini@unimore.it desire of extending the quantum mechanical method of computing chiral anomalies [6][7][8] to trace anomalies [9,10].…”

Section: Introductionmentioning

confidence: 99%

On the simplified path integral on spheres

Bastianelli

Corradini

2017

Eur. Phys. J. C

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We have recently studied a simplified version of the path integral for a particle on a sphere, and more generally on maximally symmetric spaces, and proved that Riemann normal coordinates allow the use of a quadratic kinetic term in the particle action. The emerging linear sigma model contains a scalar effective potential that reproduces the effects of the curvature. We present here further details of the construction, and extend its perturbative evaluation to orders high enough to read off the type-A trace anomalies of a conformal scalar in dimensions d = 14 and d = 16.

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“…The complete counterterm was found in [33,34]. The extensions to N = 1 and N = 2 were studied in [18] and [19], respectively.…”

Section: Introductionmentioning

confidence: 99%

Mode regularization forN= 1, 2 SUSY Sigma model

Bonezzi

Falconi

2008

J. High Energy Phys.

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Worldline N=1 and N=2 supersymmetric sigma models in curved background are useful to describe spin one-half and spin one particles coupled to external gravity, respectively. It is well known that worldline path integrals in curved space require regularization: we present here the mode-regularization for these models, finding in particular the corresponding counterterms, both in the case of flat and curved indices for worldline fermions. For N=1, using curved indices we find a contribution to the counterterm from the fermions that cancels the contribution of the bosons, leading to a vanishing total counterterm and thus preserving the covariance and supersymmetry of the classical action. Conversely in the case of N=2 supersymmetries we obtain a non-covariant counterterm with both curved and flat indices. This work completes the analysis of the known regularization schemes for N=1,2 nonlinear sigma models in one dimension.

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Dimensional regularization of nonlinear sigma models on a finite time interval

Cited by 28 publications

References 20 publications

6D trace anomalies from quantum mechanical path integrals

6D trace anomalies from quantum mechanical path integrals

On the simplified path integral on spheres

Mode regularization forN= 1, 2 SUSY Sigma model

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