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A New Representation Formula for the Bernoulli Numbers
AbstractIn this paper, we present a presumably new representation of the Bernoulli numbers. We also give an elementary proof of the Akiyama-Tanigawa...
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A thermal product formula
We show that holographic thermal two-sided two-point correlators take the form of a product over quasi-normal modes (QNMs). Due to this fact, the...
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The Basso-Dixon formula and Calabi-Yau geometry
We analyse the family of Calabi-Yau varieties attached to four-point fishnet integrals in two dimensions. We find that the Picard-Fuchs operators for...
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The Källén-Lehmann representation in de Sitter spacetime
We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the Källén-Lehmann spectral...
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Heron’s Formula in Higher Dimensions
This paper shows how geometric algebra can be used to derive a novel generalization of Heron’s classical formula for the area of a triangle in the...
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Module intersection and uniform formula for iterative reduction of one-loop integrals
In this paper, we develop an iterative sector-level reduction strategy for Feynman integrals, which bases on module intersection in the Baikov...
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Cutkosky representation and direct integration
We present a new method of direct integration of Feynman integrals based on the Cutkosky representation of the integrals. In this representation we...
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A third representation of Feynman–Kac–Itô formula with singular magnetic vector potential
The Feynman–Kac–Itô (F–K–I) formula is a useful tool to probabilistically analyze the magnetic nonrelativistic Schrödinger semigroup. Hundertmark...
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A note on the bulk interpretation of the quantum extremal surface formula
Defining quantum information quantities directly in bulk quantum gravity is a difficult problem due to the fluctuations of spacetime. Some progress...
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New Versions of the Plemelj–Sochocki Formula in Clifford Analysis
In this paper, we give some new versions of the Plemelj–Sochocki formula under weaker condition in real Clifford Analysis which are different from...
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The KLT relation from the tree formula and permutohedron
In this paper, we generalize the Nguyen–Spradlin–Volovich–Wen (NSVW) tree formula from the MHV sector to any helicity sector. We find a close...
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Chern-Simons theory, Ehrhart polynomials, and representation theory
The Hilbert space of level q Chern-Simons theory of gauge group G of the ADE type quantized on T 2 can be represented by points that lie on the...
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Digital representation of continuous observables in quantum mechanics
AbstractTo simulate quantum systems on classical or quantum computers, the continuous observables (e.g., coordinate and momentum or energy and...
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The Veneziano Formula and the Dual Resonance Model
This chapter discusses many aspects of the celebrated Veneziano FormulaVeneziano formula, a watershed moment for the analytical S-matrix programme....
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Classical observables from the exponential representation of the gravitational S-matrix
By combining the KMOC-formalism with the exponential representation of the scattering matrix we show that the two-body scattering angle is given by...
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The Problem of Derivation of the Magnus Formula
AbstractOn the basis of the condition of the flow potentiality of the hydrodynamic stream flowing around a stationary rotating ball, a detailed...
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Dynamical actions and q-representation theory for double-scaled SYK
We show that DSSYK amplitudes are reproduced by considering the quantum mechanics of a constrained particle on the quantum group SU q (1 , 1). We...
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On the off-diagonal Wick’s theorem and Onishi formula
The projected generator coordinate method based on the configuration mixing of non-orthogonal Bogoliubov product states, along with more advanced...
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Bootstrap** Witten diagrams via differential representation in Mellin space
We explore the use of the differential representation of AdS amplitudes to compute Witten diagrams. The differential representation expresses AdS...
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Celestial self-dual Yang-Mills theory: a new formula and the OPE limit
Celestial holography is a new way to understand flat-space amplitudes. Self-dual theories, due to their nice properties, are good subjects to study...