Quantum Satake in type $A$. Part I

The Hecke category (part II—Satake equivalence)

Theorem 1. The convolution ∗ admits a commutativity constraint making Sph into a rigid tensor category. There exists a faithful, exact tensor “fiber” functor Sat : Sph → Vect inducing an equivalence (modulo a sign in the commutativity constraint) of Sph with Rep(G) as tensor categories, where G is the Langlands dual group of the reductive group G, whose weights are the coweights of G and vice v...

Quantum Electromagnetics: A New Look, Part I∗

Quantization of the electromagnetic field has been a fascinating and important subject since its inception. This subject topic will be discussed in its simplest terms so that it can be easily understood by a larger community of researchers. A new way of motivating Hamiltonian mechanics is presented together with a novel way of deriving the quantum equations of motion for electromagnetics. All e...

Distal Approaches in Patellofemoral Pain: A Systematic Review, Part I

Purpose: Increased patellofemoral joint reaction force (PFJRF) is the main cause of patellofemoral pain syndrome (PFP). Foot pronation causes faulty joint coupling of the lower limb and increases the PFJRF. Therefore, the aim of systematic review is effect of the distal interventions on the clinical symptoms and kinematic of PFP patients.   Methods: The search strategy was carried out from Goo...

Quantum decoherence in a pragmatist view: Part I

The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum probabilities as a guide to their truth. The content of a claim is to be understood in terms of its role in inferences. This promises a better treatment of meaning tha...

Chaos: Classical and Quantum Part I: DeterministicChaos