## 65 Citations

Trace dynamics, and a ground state in spontaneous quantum gravity

- Physics
- 2020

We have recently proposed a Lagrangian in trace dynamics, to describe a possible unification of gravity, Yang-Mills fields, and fermions, at the Planck scale. This Lagrangian for the unified entity…

A QUANTUM MODEL WITH ONE BOSONIC DEGREE OF FREEDOM

- Physics
- 1996

Conventionally, when we construct a quantum model, we must first know the corresponding classical model. Applying the correspondence between the classical Poisson brackets and the canonical…

A basic definition of spin in the new matrix dynamics

- Physics
- 2020

Abstract We have recently proposed a new matrix dynamics at the Planck scale, building on the theory of trace dynamics. This is a Lagrangian dynamics in which the matrix degrees of freedom are made…

Hamiltonian formulation of generalized quantum dynamics

- Physics
- 1997

The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed. After the total trace Lagrangian, total trace Hamiltonian and two kinds…

I. AN EIGENVALUE EQUATION FOR THE HAMILTONIAN OF AN AIKYON

- Physics
- 2021

We have recently proposed a Lagrangian in trace dynamics, to describe a possible unification of gravity, Yang-Mills fields, and fermions, at the Planck scale. This Lagrangian for the unified entity…

Proposal for a New Quantum Theory of Gravity

- PhysicsZeitschrift für Naturforschung A
- 2019

Abstract We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu–Goto + Kalb–Ramond string [R. T. Hammond, Rep. Prog. Phys. 65, 599 (2002)]. We explain why this…

Quartic quantum theory: an extension of the standard quantum mechanics

- Physics
- 2008

We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex…

Quantum Group Sheaf and Quantum Manifolds

- Mathematics
- 1994

The problem of introducing a dependence of elements of quantum group on classical parameters is considered. It is suggested to interpret a homomorphism from the algebra of functions on quantum group…

## References

SHOWING 1-10 OF 41 REFERENCES

QUANTIZATION OF THE YANG-MILLS FIELD

- Physics
- 1962

The Yang-Mills field, a gauge-type nonlinear field which lies between electrodynamics and general relativity in complexity is examined. The quantum Yang-Mills field is introduced to satisfy the…

Principle of General Q Covariance

- Mathematics
- 1963

In this paper the physical implications of quaternion quantum mechanics are further explored. In a quanternionic Hilbert space HQ, the lattice of subspaces has a symmetry group which is isomorphic to…

Proof of Jacobi identity in generalized quantum dynamics

- Physics
- 1994

It is proven that the Jacobi identity for the generalized Poisson bracket is satisfied in the generalization of Heisenberg picture quantum mechanics recently proposed by one of the authors. The…

Quantum models without canonical quantization

- Physics
- 1993

Conventional approach to constructing a quantum model, consisting in canonical quantization of a related classical model,can be applied only if we know the classical model and its Hamiltonian…

Projection operators and states in the tensor product of quaternion hilbert modules

- Mathematics
- 1991

Following the construction of tensor product spaces of quaternion Hilbert modules in our previous paper, we define the analogue of a ray (in a complex quantum mechanics) and the corresponding…

Quaternionic quantum mechanics and quantum fields

- Physics
- 1995

PART I: INTRODUCTION AND GENERAL FORMALISM 1: Introduction 2: General Framework of Quaternionic Quantum Mechanics 3: Further General Results in Quaternionic Quantum Mechanics PART II:…

Tensor product of quaternion hilbert modules

- Mathematics
- 1991

One of the main problems in the theory of quaternion quantum mechanics has been the construction of a tensor product of quaternion Hilbert modules. A solution to this problem is given by studying the…

Uniqueness of the scalar product in the tensor product of quaternion Hilbert modules

- Mathematics
- 1992

In the construction of a tensor product of quaternion Hilbert modules, given in a previous work (real, complex, and quaternionic), inner products were defined in the vector spaces formed from the…