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Constraints on Effective Field Theories Without Lorentz Invariance
Constraints on Effective Field Theories Without Lorentz Invariance
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202104816
- ISBN
- 9798290937250
- DDC
- 530
- 저자명
- Zhou, Shengjia.
- 서명/저자
- Constraints on Effective Field Theories Without Lorentz Invariance
- 발행사항
- [Sl] : Columbia University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 154 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-02, Section: B.
- 주기사항
- Advisor: Nicolis, Alberto.
- 학위논문주기
- Thesis (Ph.D.)--Columbia University, 2025.
- 초록/해제
- 요약Effective Field Theory is a powerful tool to understand low-energy physics. Constraining effective field theories without Lorentz invariance is an open question. In this thesis, we study two different approaches to constrain effective field theories without Lorentz invariance. The first approach is to study analytic structures of scattering amplitudes without Lorentz invariance. The second approach is to consider the implications of microcausality. In the study of the first approach, we study the scattering amplitude in a simple example: a superfluid described by a complex scalar field with quartic interactions. We compute the 2 → 2 scattering amplitude of gapless excitations at tree-level. In the center of mass configuration, we find that crossing symmetry is lost, and there is a branch cut on the complex s plane at tree level. Furthermore, all the even derivatives of the forward scattering amplitude at s = 0 are positive, while all the odd derivatives are negative. This pattern of the derivatives of the scattering amplitude can be derived in a more general theory in the limit of weak Lorentz breaking effect.In the second approach, we derive implications of microcausality on two-point correlation functions. For the commutator Green's function, microcausality implies that its Fourier transform is analytic for all complex momentum and satisfies an exponential boundedness condition. We derive a similar result for the retarded Green's function. We verify these properties in several examples, including Lorentz invariant theories, a free non-relativistic scalar field theory, a UV-complete model of a relativistic superfluid, and scalar fields in de Sitter space. In addition, we derive a constraint on the effective field theory of inflation. Finally, we discuss the possibility of constraining higher-point correlation functions from microcausality.
- 일반주제명
- Physics
- 일반주제명
- Applied mathematics
- 일반주제명
- Energy
- 일반주제명
- Fluid mechanics
- 키워드
- Microcausality
- 키워드
- Green's function
- 키워드
- Superfluids
- 기타저자
- Columbia University Physics
- 기본자료저록
- Dissertations Abstracts International. 87-02B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798290937250
■035 ▼a(MiAaPQ)AAI32168410
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530
■1001 ▼aZhou, Shengjia.
■24510▼aConstraints on Effective Field Theories Without Lorentz Invariance
■260 ▼a[Sl]▼bColumbia University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a154 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-02, Section: B.
■500 ▼aAdvisor: Nicolis, Alberto.
■5021 ▼aThesis (Ph.D.)--Columbia University, 2025.
■520 ▼aEffective Field Theory is a powerful tool to understand low-energy physics. Constraining effective field theories without Lorentz invariance is an open question. In this thesis, we study two different approaches to constrain effective field theories without Lorentz invariance. The first approach is to study analytic structures of scattering amplitudes without Lorentz invariance. The second approach is to consider the implications of microcausality. In the study of the first approach, we study the scattering amplitude in a simple example: a superfluid described by a complex scalar field with quartic interactions. We compute the 2 → 2 scattering amplitude of gapless excitations at tree-level. In the center of mass configuration, we find that crossing symmetry is lost, and there is a branch cut on the complex s plane at tree level. Furthermore, all the even derivatives of the forward scattering amplitude at s = 0 are positive, while all the odd derivatives are negative. This pattern of the derivatives of the scattering amplitude can be derived in a more general theory in the limit of weak Lorentz breaking effect.In the second approach, we derive implications of microcausality on two-point correlation functions. For the commutator Green's function, microcausality implies that its Fourier transform is analytic for all complex momentum and satisfies an exponential boundedness condition. We derive a similar result for the retarded Green's function. We verify these properties in several examples, including Lorentz invariant theories, a free non-relativistic scalar field theory, a UV-complete model of a relativistic superfluid, and scalar fields in de Sitter space. In addition, we derive a constraint on the effective field theory of inflation. Finally, we discuss the possibility of constraining higher-point correlation functions from microcausality.
■590 ▼aSchool code: 0054.
■650 4▼aPhysics
■650 4▼aApplied mathematics
■650 4▼aEnergy
■650 4▼aFluid mechanics
■653 ▼aEffective field theory
■653 ▼aLorentz invariance
■653 ▼aMicrocausality
■653 ▼aGreen's function
■653 ▼aSuperfluids
■690 ▼a0605
■690 ▼a0204
■690 ▼a0364
■690 ▼a0791
■71020▼aColumbia University▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g87-02B.
■790 ▼a0054
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17358966▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
