Zobrazeno 1 - 10
of 773
pro vyhledávání: '"Lachapelle J"'
Autor:
LaChapelle, J.
$U(n)$ is a semi-direct product group that is characterized by non-trivial homomorphisms mapping $U(1)$ into the automorphism group of $SU(n)$. For $U(3)$, there are three non-trivial homomorphisms that induce three separate defining representations.
Externí odkaz:
http://arxiv.org/abs/2206.02557
Autor:
LaChapelle, J.
Restricting attention to kinematics, we develop the $C^\ast$-algebraic quantum mechanics of $Sp(8,\mathbb{C})$. The non-compact group does double duty: it furnishes the quantum Hilbert space through induced representations, and it spawns the quantum
Externí odkaz:
http://arxiv.org/abs/1902.10531
Autor:
LaChapelle, J.
Zeros and poles of $k$-tuple zeta functions, that are defined here implicitly, enable localization onto prime-power $k$-tuples in pair-wise coprime $k$-lattices $\mathfrak{N}_k$. As such, the set of all $\mathfrak{N}_k$ along with their associated ze
Externí odkaz:
http://arxiv.org/abs/1812.03836
Autor:
LaChapelle, J.
We examine the Standard Model under the electroweak symmetry group $U_{EW}(2)$ subject to the Lie algebra condition $\mathfrak{u}_{EW}(2)\not\cong \mathfrak{su}_{I}(2)\oplus \mathfrak{u}_{Y}(1)$. Physically, the condition ensures that all electroweak
Externí odkaz:
http://arxiv.org/abs/1709.04346
Autor:
LaChapelle, J.
We propose $Sp\,(8,\R)$ and its Langlands dual $SO(9,\R)$ as dynamical groups for closed quantum systems. Restricting here to the non-compact group $Sp\,(8,\R)$, the quantum theory is constructed and investigated. The functional Mellin transform play
Externí odkaz:
http://arxiv.org/abs/1506.02985
Autor:
LaChapelle, J.
Conventional functional/path integrals used in physics are most often defined as the infinite-dimensional analog of Fourier transform. Likewise, the infinite-dimensional analog of Mellin transform also defines a class of functional integrals. The ass
Externí odkaz:
http://arxiv.org/abs/1501.01889
Autor:
LaChapelle, J.
Functional integrals can be defined on topological groups in terms of families of locally compact topological groups and their associated Banach-valued Haar integrals. The definition forgoes the goal of constructing a genuine measure on a space of fu
Externí odkaz:
http://arxiv.org/abs/1501.01602
Autor:
LaChapelle, J.
Starting with Zhang's theorem on the infinitude of prime doubles, we give an inductive argument that there exists an infinite number of prime $k$-tuples for at least one admissible set $\mathcal{H}_k=\{h_1,\ldots,h_k\}$ for each $k$.
Comment: up
Comment: up
Externí odkaz:
http://arxiv.org/abs/1406.6619
Autor:
LaChapelle, J.
We conjecture average counting functions for prime $k$-tuples based on a gamma distribution hypothesis for prime powers. The conjecture is closely related to the Hardy-Littlewood conjecture for $k$-tuples but yields better estimates. Possessing avera
Externí odkaz:
http://arxiv.org/abs/1406.6289
Autor:
LaChapelle, J.
Exact summatory functions that count the number of prime $k$-tuples up to some cut-off integer are presented. Related $k$-tuple analogs of the first and second Chebyshev functions are then defined.
Comment: arXiv admin note: text overlap with ar
Comment: arXiv admin note: text overlap with ar
Externí odkaz:
http://arxiv.org/abs/1406.5533