realms of Hadamard spaces

[AntonioLao]

In a differentiable n-dimensional real manifold, the state space or phase space of a quantum-mechanical system is a linear n-dimensional Euclidean space whose elements are disjointed real vectors or tensors. Its generalization into a differentiable n-dimensional complex manifold is called a functional Hilbert space whose elements are complex vectors, spinors, or twistors. This general space is a singular isolated quantum system. Nonetheless, a symmetry principle exists, such that it asserts the simultaneous existence of two isolated quantum systems whose state vectors are equal and opposite, by sign differences (positive and negative) in the real field and conjugates in the complex field. Their products become Hadamard spaces whose elements are singular (zero determinants) symmetric matrices of infinite orders. These are basically curvilinear spaces (nonlinear and nonfunctional – many to many correspondence). They generalize representations for squares of energy at varying LOEs (levels of existence). Their additive operations give space-time charges and multiplicative operations give space-time masses. The governing local gauge symmetry principle is a principle of directional invariance. This is equivalent to the supposed global symmetry of general relativity known as general covariance. However, general covariance makes more sense if it is applied locally at the infinitesimal gauge level of a quantum field with infinite degrees of freedom.

[mkirkpatrick]

I did not understand much of what you said Antonio,but it seems that you
may be on to something?Am I right!or am I right!Maths are not my strong point.


kind regards michael.

[AntonioLao]

but it seems that you may be on to something?Am I right!or am I right!

My objective is to attain fusion whether using hot or cold process. The lead I am following is the quantization of charge and mass or space-time quantization.