FREYMAN'S INTEGRAL PATHWAY

freyman’s integral pathway (p,q) = e-1/4 (p+q2)S[(q+ip)/ 2]/ n!


quantum particles have more freedom
than their classic counterparts and

all the information about any
autonomous quantum particles
is contained within the
matrix of elements of its
time evolution operator

the time evolution operator
describes this dynamic evolution
under the influence of
Hamiltonian time

H = T + V or H = E + R

where R is a positive definite
real symmetric n-dimensional
matrix and V is a real vector
diagonalized by orthogonal transformation
into E mono-kinetic Euclidean

as the matrix elements express
amplitude for a particle to
propagate between points
it becomes the propagator
of harmonic oscillation

often one encounters integrals
where the exponent is not purely quadratic
from the outset but rather contains
both quadratic and linear pieces

to prove this identity
eliminate the linear term
the constant factor scales a-z
yet quantum mechanics remains
fully present

it is the incoherent super-position
of different integral faiths that
destructively interferes with the
language of quantum mechanics

[we] insert position and momentum
respectively making use of
the clear rationale behind
the resolution of vector identity

in the matrix of elements
the discrete set becomes dense
over time and space becomes
a continuous curve

this smooth variation of paths
contributes significantly toward
the motivation and the application
of a continuum limit [less]

proving that u and I may be
independent complex numbers
that need not be related by the
simple conjugation of
coherent states and
paths integral

only by love.



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