41 citations · 66 across the 22 of their papers we have counts for
23 papers
The Three Faces of
J. LaChapelle
is a semi-direct product group that is characterized by non-trivial homomorphisms mapping into the automorphism group of . For , there are three non-triv…
Apparent Geometry from the Quantum Mechanics of
J. LaChapelle
Restricting attention to kinematics, we develop the -algebraic quantum mechanics of . The non-compact group does double duty: it furnishes the quantum Hil…
A Note on Counting Lattice Points in Bounded Domains
J. LaChapelle
Zeros and poles of -tuple zeta functions, that are defined here implicitly, enable localization onto prime-power -tuples in pair-wise coprime -lattices . A…
A non-Standard Standard Model
J. LaChapelle
We examine the Standard Model under the electroweak symmetry group subject to the Lie algebra condition $\mathfrak{u}_{EW}(2)\not\cong \mathfrak{su}_{I}(2)\oplus \mathf…
Functional Integral Approach to -algebraic Quantum Mechanics II: Symplectic Quantum Mechanics
J. LaChapelle
We propose and its Langlands dual as dynamical groups for closed quantum systems. Restricting here to the non-compact group , the quantum theory…
Functional Integral Approach to -algebraic Quantum Mechanics I: Heisenberg and Poincaré
John LaChapelle
The algebraic approach to quantum mechanics has been vital to the development of quantum theory since its inception, and it has evolved into a mathematically rigorous -alge…