Научная статья на тему 'ZERO-RANGE POTENTIALS: DELTA-LIKE BARRIER VERSUS SELF-ADJOINT EXTENSION'

ZERO-RANGE POTENTIALS: DELTA-LIKE BARRIER VERSUS SELF-ADJOINT EXTENSION Текст научной статьи по специальности «Науки о Земле и смежные экологические науки»

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Ключевые слова
SINGULAR POTENTIAL / SELF-ADJOINT EXTENSION / ZERO-WIDTH INTERACTION / RENORMALIZATION

Аннотация научной статьи по наукам о Земле и смежным экологическим наукам, автор научной работы — Grats Yu.V., Spirin P.

We compare two different approaches to compute the effects of vacuum polarization associated with a massless scalar eld near pointlike source with a zero-range potential in three spatial dimensions. The first one consists in the usage of delta-like sequence of regular potentials, regarding the limit as a model of pointlike interaction. We use the Perturbation theory in the Fourier space. The second approach implies the self-adjoint extension technique. We compute the renormalized vacuum expectation value of the eld square \φ 2 (x))ren in non-perturbative sense.

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Текст научной работы на тему «ZERO-RANGE POTENTIALS: DELTA-LIKE BARRIER VERSUS SELF-ADJOINT EXTENSION»

20th LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS

39

Field Interpretation of General Relativity Revisited

Michael Fil'chenkova, Yuri Laptev E-mail: afmichael@mail.ru

Institute of Gravitation and Cosmology, RUDN University. Moscow, 117198, Russia

Received January 16, 2022

A field interpretation of General Relativity has been presented for a static field of black holes and de Sitter's vacuum describing dark energy. The gravitational potential satisfies Poisson's equation. Einstein-Hilbert's equations in these cases prove to be superfluous.

Keywords: general relativity, Poisson's equation, black holes, dark energy.

English version: Moscow University Physics Bulletin. 2022. 77, No. 2. Pp. 446-447.

Zero-Range Potentials: Delta-Like Barrier Versus Self-Adjoint Extension

Yu.V. Gratsa, P.Spirin E-mail: agrats@phys.msu.ru

Physics Department, Lomonosov Moscow State University. Moscow, 119991, Russia

Received January 9, 2022

We compare two different approaches to compute the effects of vacuum polarization associated with a massless scalar field near pointlike source with a zero-range potential in three spatial dimensions. The first one consists in the usage of delta-like sequence of regular potentials, regarding the limit as a model of pointlike interaction. We use the Perturbation theory in the Fourier space. The second approach implies the self-adjoint extension technique. We compute the renormalized vacuum expectation value of the field square (^2(x)}ren in non-perturbative sense.

Keywords: singular potential, self-adjoint extension, zero-width interaction, renormalization.

English version: Moscow University Physics Bulletin. 2022. 77, No. 2. Pp. 448-450.

Complete Vectorlike Fourth Family and New U(1)' for Muon Anomalies

Junichiro Kawamura E-mail: jkawa@ibs.re.kr

Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS). Daejeon 34051, Korea

Received January 16, 2022

I introduce a model to explain the recent anomalies in the muon anomalous magnetic moment and the rare semi-leptonic B meson decays. The Standard Model is extended by a U(1)' gauge symmetry and a complete fourth family fermions which are vector-like under the gauge symmetry. We found parameter points which can explain the anomalies consistently with the other observables. We then propose an interesting possibility to have signals with four muons or more from vector-like lepton pair production.

Keywords: : muon anomalies, gauge symmetry, charged leptons, lepton flavor violation.

English version: Moscow University Physics Bulletin. 2022. 77, No. 2. Pp. 451-455.

Quantum Electrodynamics with y5 Modified Dirac Field

Galina A. Kravtsova1'0,, Vasily N. Rodionov2'6 E-mail: agakr@chtc.ru, 6rodyvn@mail.ru

1 Physics Department, Lomonosov Moscow State University. Moscow, Russia 2Moscow Humanitarian University. Moscow, Russia Received January 14, 2022

The interaction of 75-modified Dirac fields with electromagnetic field is introduced. The possible gauge invariance is studied.

Keywords: modified Dirac field, maximal mass.

English version: Moscow University Physics Bulletin. 2022. 77, No. 2. Pp. 456-457.

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