Geri Dön

Batalin-Fradkin-Vilkovisky metodu ile bağlı sistemlerdeki iz-integrallerinin hesaplanma yöntemi

Calculation of the path integrals in constrained systems by the Batalin-Fradkin-Vilkovisky method

  1. Tez No: 14137
  2. Yazar: NEŞE ÖZDEMİR
  3. Danışmanlar: PROF.DR. MAHMUT HORTAÇSU
  4. Tez Türü: Yüksek Lisans
  5. Konular: Fizik ve Fizik Mühendisliği, Physics and Physics Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1990
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 53

Özet

ÖZET İki bölümden oluşan bu çalışmada, bağ koşullu alanlar için BFV kuantizasyon metodu incelenmiştir. İlk bolüm, üç kısımdan oluşmaktadır. Birinci kısımda Global olarak bir sis temin değişmezliği incelenmiş ve bu değişmezlik için iki formalizm açıklanmıştır; Lagrange ve Hamilton formalizmi. Ayrıca Lagrange fonksiyonunun değişmez olması için gerekli koşullar gözönüne alınmıştır. İlk bolümün ikinci kısmında yerel olarak değişmezlikler ele alınmış ve yerel olarak değişmez olan Lagrange fonksiyonları anlatılmıştır. Lagrange fonksiyonunu yerel olarak değişmez kılmak için yardıma alanlara ihtiyacımız olduğu vurgulanmıştır. Lagrange fonksiyonunun değişmez kalmasının neden olduğu akım korunumlan da bu bolümde anlatılmıştır. Birinci bölümün son kısmında iz-integrali ve geçiş genliği anlatılmış ve üzerinde bağ koşulları tanımlanmamış serbest alanlar ve bağ koşullu alanlar için bu hesaplamalar yapılmıştır, ikinci bolüm, dört alt kısımdan oluşmaktadır. Birinci kısımda BFV formalizminin ne olduğu anlatılmış, ikinci kısımda ise bu formalizmde ortaya çıkan bir ayar- belirleme fonksiyonu elde edilmiştir. Üçüncü kısımda Fradkin-Vilkovisky teoremi ifade edilmiş ve bu teoremin ancak bir noktaya kadar doğru olabileceği anlatılmıştır. BFV metodunu basit bir örnek için; relativistik skaler parçacık örneği için dördüncü kısımda inceledik ve“ iyi n ve ”kötü * ayar-belirleme fonksiyonlarına örnekler vererek Fradkin-Vilkovisky teoremi ile. çelişen yönünü açıkladık. iv

Özet (Çeviri)

CALCULATION OF THE PATH INTEGRALS IN CONSTRAINED SYSTEMS BY THE BATALIN-FRADKIN-VILKOVISKY METHOD SUMMARY In recent years, gauge fields have attrached much attention in elementary particle physics. The reason is that great progress has been achieved in solving a number of important problems of field theory and elementary particle physics by means of quantization of gauge fields. Using the symmetries corresponding to the local groups interesting pos sibilities arise in the realization of this idea. To construct locally invariant theories, new fields have to be introduced which are referred as gauge fields. The first step in constructing a gauge invariant theory is to find the gauge invariant Lagrangians. This is dealt with in Chapter 1. and we give a brief account of fundamentals of the global invariance and globally invariant La grangians. A general method of constructing the gauge invariant Lagrangians is given, along with the basic properties of the gauge fields. After obtaining the expressions for the Lagrangian, we pass to constructing the quantum the ory of gauge fields (in section 2.). Furthermore, the major properties of the gauge fields are clarified. It turns out that in solving these problems the re quirement of invariance under the group of local transformations is sufficient. We know that., there are various formulations of quantum field theory, differ ing in the form of a basic quantity; the transition amplitude. The transition amplitude can be expressed as the vacuum expectation value of the product, of particle creation and annihilation operators. Another formulation is based on expressing the transition amplitude in terms of path-integrals over the fields. In studying the gauge fields, the path-integral formalism has proven to be the most convenient. And the expressions for the transition amplitude are found in terms of the path-integral (in section 3). We find the expressions for the amplitude of the vacuum-vacuum tran sition in terms of the path-integral formalism and we start by considering unconstrained fields and then go over to fields with constraints. Gauge fields belong to the latter type. At the end of this chapter, we mention few factsabout constraints. Our aim is to find an exression for the matrix elements of the evolution operator in form of path-integrals under these conditions, i.e for generalized Hamilton systems. The path-integral for unconstrained systems can be written as (2A. In Chapter 2. we consider to what extend the BFV path-integral depends on the gauge-fhdng function. Contrary to what is usually stated, it will be ar gued that there is some dependence, so that the gauge-fixing of such systems has to be done appropriately. A short review of the BFV7 formalism is given in section 1. In this section, we enlarged phase-space in two steps. Further more, because the physical observables are simply BRST invariant quantities, i.e their Poisson brackets with Qb vanishes, we introduced BRST invariant Hamilton! an SB = H0 + T)aV?Pb +“more”and Physical states are obtained as states annihilated by the BRST charge (i.e they correspond to the cohomology classes of Qb)-. and of zero ghost number, provided Qb is nilpotent at the quantum level: QB\nrtr) = 0. After enlarging the physical Hubert space representation of the quantum sys tem, we obtain a phase-space path-integral representation for any observable. This BFV path-integral over the extended phase-space is taken with the Liou- ville measure and the effective action which corresponds to the Hamiltonian. In section 2. we discuss the structure of the space of orbits of the gauge group, i.e K Teichmuller“ space and the quantity Jri ”Teichmuller w parameter which is labelling the gauge or bite of the system for gauge transformations connected to the identity transformations. Then the correct statement for the FradMn-Vilkovisky theorem, which determines the dependence of the BFV path-integral on the gauge-fixing func tion, is considered in section 3. The probabilitiy amplitude to Kpropagete“ VIIfrom a configuration q^h) to a configuration ^(ii) is given by Z = [qHhlqHh)) = J[Dti}eiS*ira + Xy?'», ”&aX“ ürf}. At âs And the dependence of gauge equivalence classes on gauge-fixing functions aje seen from these examples. We see that the BFV path-integral does not specifically depend on a given gauge-fixing function,but that it depends on its gauge equivalence class. The BRST idependence of BFV path-integral does not. mean that it is independent of gauge-fixing function. The correct, gauge- invariant path-integral is given by the BFV path-integral only when evaluated for the gauge-equvalence class of ”good“ gauge-fixing functions. This equiv alence class does not exist, when the. description of the system suffers from a Gribov problem. As LSinger pointed out if one defines the path-integral on the surface of a sphere in Euclidean space, 54; the Gribov problem is endemic and its causes lies in the fact, that it is not possible to get away with the same gauge condition over all of space time. In section 4. we illustrate our arguments in the case of a simple system: the Telativistic scalar particles. Furthermore, we show that if //(c) is equal to 1, which is an undetermined integration measure, the BFV path-integral is the * good w gauge-equivalence class. And we see that the BFV path-integral BRST invariant, i.e it is independent of the specific point on the gauge orbit at which the gauge-fixing is done. All gauge inequivalent configurations of the system are characterized by all points in modular space. A complete gauge fixing of the system is thus determined by a gauge slice in the space of Lagrange multipliers which selects, for each point modular space, one and only one representative (A°(i)) for one and only one gauge orbit in the equivalence class correspondig to that point in modular space. For a function 4! which would achieve such acomplete gauge-fixing, the path-integral, as given above, would reduce to an integral over modular space, giving a gauge invariant representation of the corresponding quantum observable. However, as the BFV formalism explicitly incorporates only the gauge Vllltransformations connected to the identity at best there may exist gauge- fixing functions ip such that the path-integral reduces to an integral over ”Te- ichmüller' space. We will refer to such functions $ as“good* gauge-fixing functions. In practice, this does not lead to a problem the correct gauge in variant quantity is obtained by ”moding out.“ the integral over TeichmiiBer space by the modular group, i.e by restricting the integral to afundamental domain of the modular group in Teichmülller”space. At the conclusion part, we show, how the correct gauge-invariant path- integral representation of a physical observable must reduce, to an integral over modular space (the space of gauge orbits), through the evolution of the. path- integral for the gauge-equivalence class of“ good n gauge-fixing functions. For systems which suffer from a Gribov problem, although such ”good w gauge-fixing functions do not exist, we discussed how the correct quantities can nevertheless be obtained, up to an undetermined integration measure over modular space. We should also mention that interesting developments have recently been achieved concerning this system in the attempt of understanding the funda mental role played by BRST symmetry in gauge-invariant systems better. IX

Benzer Tezler

  1. Tez No

    47208

    On the theory of fermions interacting through the chern-simons gauge field

    Chern-Simons ayar alanı vasıtası ile etkileşen fermionlarının teorisi üzerine

    MOHAMMAD SHİKAKHWA

    Doktora

    İngilizce

    İngilizce

    1995

    Fizik ve Fizik MühendisliğiOrta Doğu Teknik Üniversitesi

    PROF.DR. NAMIK KEMAL PAK

    PROF.DR. VLADİMİR FAİNBERG

  2. Tez No

    38607

    Path integral quantization of the theory of scalar charged particles interacting via chern-simons fields and its application

    Chern simons alanları aracılığı ile etkileşen skaler yüklü parçacıklar teorisinin yol integral kuantizasyonu ve uygulamaları

    MÜGE BOZ

    Doktora

    İngilizce

    İngilizce

    1995

    Fizik ve Fizik MühendisliğiOrta Doğu Teknik Üniversitesi

    PROF.DR. NAMIK KEMAL PAK

  3. Tez No

    829775

    Көркөм фильмдердеги тарыхыйреалияларды которуу маселелери(«эртугрул» көп сериалдуу фильмининкыргызча котормосунун негизинде)

    Filmlerdeki tarihi kültürel öğeleri aktarma sorunları («Diriliş Ertuğrul» dizisinin Kırgızca çevirisinin örneğinde)

    BAYALİN KASIMALİ UULU

    Yüksek Lisans

    Kırgızca

    Kırgızca

    2023

    Mütercim-TercümanlıkKırgızistan-Türkiye Manas Üniversitesi

    Mütercim Tercümanlık Ana Bilim Dalı

    DR. ÖĞR. ÜYESİ KALİYA KULALİYEVA

  4. Tez No

    130026

    Kur'an'da furkan kavramı

    The Term of furqan in the Holy Qur'an

    İSMAİL AYDIN

    Yüksek Lisans

    Türkçe

    Türkçe

    2003

    DinDokuz Eylül Üniversitesi

    Temel İslam Bilimleri Ana Bilim Dalı

    PROF. DR. ÖMER DUMLU

  5. Tez No

    530694

    Sabır kavramının semantik tahlili

    Semantics analysis of the concept of patience

    HALİL İBRAHİM KAHRAMAN

    Yüksek Lisans

    Türkçe

    Türkçe

    2018

    DinEskişehir Osmangazi Üniversitesi

    Temel İslam Bilimleri Ana Bilim Dalı

    DR. ÖĞR. ÜYESİ FATİH TOK

Geri Dön