2025/02/04 by Joao Penedones, João Penedones, Kamran Salehi Vaziri +1 · 16 citations
Mathematics · Physics and Astronomy · #Anti-de Sitter space #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #De Sitter space #De Sitter universe #Field (mathematics) #Linguistics #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Philosophy #Physics #Pure mathematics #Quantum #Quantum field theory #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Space (punctuation) #Spacetime #Theoretical physics #Universe #de Sitter invariant special relativity #de Sitter–Schwarzschild metric
paper · doi:10.1103/physrevd.111.045001
published in Physical review. D/Physical review. D. 111(4) (American Physical Society)
openalex publication_date 2025/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study the decomposition of the Hilbert space of quantum field theory in ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>d</a:mi> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> )-dimensional de Sitter spacetime into unitary irreducible representations (UIRs) of its isometry group <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi>SO</c:mi> <c:mo stretchy="false">(</c:mo> <c:mn>1</c:mn> <c:mo>,</c:mo> <c:mi>d</c:mi> <c:mo>+</c:mo> <c:mn>1</c:mn> <c:mo stretchy="false">)</c:mo> </c:mrow> </c:math> . First, we consider multiparticle states in free theories starting from the tensor product of single-particle UIRs. Second, we study conformal multiplets of a bulk conformal field theory with symmetry group <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mi>SO</g:mi> <g:mo stretchy="false">(</g:mo> <g:mn>2</g:mn> <g:mo>,</g:mo> <g:mi>d</g:mi> <g:mo>+</g:mo> <g:mn>1</g:mn> <g:mo stretchy="false">)</g:mo> </g:mrow> </g:math> . Our main tools are the Harish-Chandra characters and the numerical diagonalization of the (truncated) quadratic Casimir of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mi>SO</k:mi> <k:mo stretchy="false">(</k:mo> <k:mn>1</k:mn> <k:mo>,</k:mo> <k:mi>d</k:mi> <k:mo>+</k:mo> <k:mn>1</k:mn> <k:mo stretchy="false">)</k:mo> </k:mrow> </k:math> . We introduce a continuous density that encodes the spectrum of irreducible representations contained in a reducible one of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>SO</o:mi> <o:mo stretchy="false">(</o:mo> <o:mn>1</o:mn> <o:mo>,</o:mo> <o:mi>d</o:mi> <o:mo>+</o:mo> <o:mn>1</o:mn> <o:mo stretchy="false">)</o:mo> </o:math> . Our results are complete for <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>d</s:mi> <s:mo>=</s:mo> <s:mn>1</s:mn> </s:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>d</u:mi> <u:mo>=</u:mo> <u:mn>2</u:mn> </u:math> . In higher dimensions, we rederive and extend several results previously known in the literature. Our work provides the foundation for future nonperturbative bootstrap studies of quantum field theory in de Sitter spacetime.