Why do we care about simplicity of the spectrum in Oseledets’ theorem?

Oseledets’ theorem is a fundamental result in Ergodic theory (see for example here, or Chapter 4 of Lectures on Lyapunov Exponents by Marcelo Viana). The simplicity of the spectrum has been studied by Guivarc’h and Raugi ’86, Gol’dsheid and Margulis ’89, Bonatti-Viana ’04, Avila-Viana ’07 and very recently by Mauricio Poletti. My* questions are: What … Read more

reference for higher spin – not gravitational nor stringy

Other than the papers of Berends, Burgers and van Dam, are there any papers that study the general case of deforming a free field theory with higher spin fields to be interactive? Answer Aspects of Higher-Spin Theory with Fermions, Gustavo Lucena Gómez (2014). AttributionSource : Link , Question Author : Jim Stasheff , Answer Author … Read more

About using the character formula for $SO(2n)$

I have known of the following equation for characters of a $SO(2n)$ representation with highest weights $(h_1,…,h_n)$ and for $(t_1,t_2,..,t_n,t_1^{-1},t_2^{-1},..,t_n^{-1})$ being the eigenvalues of the matrix under consideration, $$\chi (h_i,t_i) = \frac{\det (\sinh [ t_i(h_j + n-j)]) + \det (\cosh [ t_i(h_j + n-j)]) }{\det (\sinh [t_i(n-j)]) } $$ But when actually trying to put … Read more

Sites for seeking possible collaborations [closed]

Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for MathOverflow. Closed 4 years ago. Improve this question As a material scientist, I have recently constructed algorithms for solving ground state of arbitrary cluster interactions models and prepared publications in the field … Read more

Experiments physically performable in a finite amount of time whose results are independent of ZFC [closed]

Closed. This question needs details or clarity. It is not currently accepting answers. Want to improve this question? Add details and clarify the problem by editing this post. Closed 4 years ago. Improve this question In On independence and large cardinal strength of physical statements we see that their are physical statements which are independent … Read more

Why Chern numbers (integral of Chern class) are integers?

I am a physics student trying to self-learn Chern numbers and Chern class. The book I am learning (Nakahara) introduces the total Chern class as an invariant polynomial of local curvature form F P(F)=det and each {P_j}(F) defines the j-th Chern class {c_j}(F) \in {H^{2j}}(M) The book didn’t mention anything about the Chern number. According … Read more

Gauge-theoretic formulation of Maxwell equations [duplicate]

This question already has answers here: Maxwell’s equations and differential forms (11 answers) Closed 7 years ago. Does any one know how to write the Maxwell equations as an equation on a principal U(1)-bundle? In Freed & Uhlenbeck’s Instantons and Four manifolds, the authors claim that the Maxwell equations can be written in a gauge … Read more

Impact of LHC on math ? [closed]

Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for MathOverflow. Closed 9 years ago. Improve this question LHC (Large Hadron Collider) “… remains one of the largest and most complex experimental facilities ever built”. May be it is even the most … Read more

Two point function of a free scalar field in Euclidean space-time

This question was previously asked here https://physics.stackexchange.com/questions/251927/two-point-function-of-a-free-massless-scalar-field-in-euclidean-space-time though I did not get there an answer. Let ϕ(x) be a quantum free massless scalar field (i.e. operator valued function) on a Euclidean space-time of dimension D>2. Thus it satisfies the equation Δϕ(x)=0, where Δ=∑Di=1(∂i)2 is the Laplacian. I would like to compute the function D(x):=⟨0|ϕ(x)ϕ(0)|0⟩ (there … Read more

SS-matrix in QED in 2d space-time

I am not completely sure that this question is appropriate for this site, but I have asked a similar question here https://physics.stackexchange.com/questions/271372/s-matrix-in-qed-in-2d-space-time and did not get an answer. Also on this site I got in the past some nice answers to questions related to physics. I am interested in the S-matrix in QED in 2-dimensional … Read more