General talk about software patterns

["Mike Beedle" <beedlem AT e-architects.com>]

[Dear friends, I am looking for feedback for a new tool and 
a set of concepts useful to Physicists that at its root 
embed "pattern" concepts: "Physics Patterns".]


I. Introduction -- Physics Patterns

I want to provide a tool or set of tools (tentatively 
called "Physics Patterns") that:
      
   facilitate the theoretical and computational
   elementary particle Physicist cycle:

   1) proposing a Lagrangian with a "valid" symmetries
   2) deciding the fields and their interactions
   3) writing the action
   4) Evaluating the path integrals with Feynman style 
   propagators/diagrams.
   5) evaluating cross sections (to be compared with experiments)

(The tool now in embryo state is based on:
Lisa: http://lisa.sourceforge.net
JLisa: http://jlisa.sourceforge.net
Maxima: http://maxima.sourceforge.net
MatLisp: http://matlisp.sourceforge.net 
and runs on CMU Lisp. It is an interpreter that parses
a Lagrangian expressed in Maxima language, and some
initial conditions data and then spits formulas 
and numbers back.)

Apocryphal stories of Richard Feynman are told saying that
he was able to compute path integrals in hours that would
take other Physicists days or even months.  Well, this 
tool in a sense, attempts to capture the "mind of Feynman", 
abstract its computational patterns towards Lagrangians 
and the evaluation of path integrals; and put it to 
work in a general context (QED, QCD, Electroweak, Standard Model, 
Gravity, String, Quantum Loop Gravity, etc.)



II. Detailed Explanation

More specifically, the tool aims at facilitating the above cycle 
using "rule-oriented" algebraic and computational software
such that a "user", a theoretical and computational Physicist, 
can:

1) propose a Lagrangian with a "valid" symmetries and
2) decide on the fields to be used (scalar, vector, tensor, 
spinor, Grassmann, etc.), and 
3) deciding on the nature of their interactions or couplings 
based on assumptions about the exchange particles: mass, spin, 
charge, color, charm, fermion number, boson number, etc.;
including renormalization group flow options.

  This validation is facilitated through a rule-oriented analysis 
  of the mathematical symmetry patterns or a "proposed 
  Lagrangian" using Lisa and Maxima in a Lisp environment.  

  The exit condition is that the "proposed Lagrangian"
  would be both "interesting but valid" in terms of its: 
     1) symmetries
     2) the viability of the proposed Fields and
     3) its exchange particles

(From a technical perspective, I might have to incorporate 
or translate to Lisp/Lisa some of the guts of a tool 
like GAP "Groups, Algorithms and Programming": 
http://www-gap.dcs.st-and.ac.uk/~gap/.
However, in some previous papers I have shown some 
equivalences of 
1) "rule-oriented" systems, 
2) group-theoretical approaches 
3) pattern-oriented approaches, (Grenander, Alexander, etc.)
4) genetic systems 
http://www.mikebeedle.com/pub/unified.pdf
http://www.livingmetaphor.org/pattern-languages-autocatalytic-
system.html
, so although *much more* can be said and one, at least 
I am not coming empty-handed into this task :-)

GAP as well as some portions of Maxima, MatLisp, are 
capable of evaluating matrix and tensor expressions 
that are relevant to Physics so that actions in
different groups (U(1), SO(2), SU(2), SO(3), 
SU(3), SO(N), SU(N)) on selected sets (complex scalars, 
vectors, spinors, tensors, Grassmann, etc.) can 
be evaluated both at the algebraic and computational
levels.

Once the Lagrangian is validated then the tool
also facilitates:

3) writing the action
4) Evaluating the path integrals with Feynman style 
   propagators/diagrams.
5) evaluating cross sections

  This can be done through "rule-oriented" calculations of 
  path integrals, that help the "user" with the computation 
  of the evaluation of path integrals related to general 
  multi-particle scatterings, both in the:

  a) algebraic sense (Maxima) with potential theoretical value, 

  and in

  b) the computational sense in the evaluation or 
  probabilities and cross sections side (MatLisp/LAPACK),
  with the potential of comparing the calculations to
  experiments in accelerators (or other natural occurring
  phenomena).

  The "back-end" architecture consists of the encoding 
  of these rules, or at least most of the rules, for 
  the creation and evaluation of "general" Feynman 
  diagrams related to the scattering of "general" 
  particles with options for masses, spins, charges, 
  colors, charm, fermion number, boson number, etc.; 
  with the hope that much sophisticated multi-particle 
  Lagrangians can be evaluated ...... 
  
    without even ever writing a formula for 
    the expansion of the path integral into 
    Feynman diagrams with propagators.  (The only thing
    required would be a configuration option to know
    at what power to stop :-)

  Every theoretician's nightmare 
  is to find and compute such an expansion.  In fact, 
  it is my belief that many Ph.D. in Physics are 
  granted with what this tool will eventually be 
  able to do in possibly .... hours if not minutes.

  Most of the rules above, both in the Lagrangian validation,
  and in the evaluation of the path integrals for
  different interactions Electroweak, Strong (primitive,
  residual), Gravity are in fact _known_, so the initial
  work would be more of an "encoding and testing job" 
  rather than a research work per se.  (Thousands of 
  computations and experimental results abound!!)

  My plan is to start with QED, then move to 
  the Electroweak expansion, then QCD and the Standard
  Model, and eventually try things like String, LQG 
  (Loop Quantum Gravity).


III. RESEARCH

Up to this point, none of the above could be considered 
"true research" -- because it would mostly be 
"automation of tedious but *known* work" i.e. a theoretical
or computational Physicist with enough time would 
calculate both the expressions and the cross sections
for a given setup.

However, the research side of it, once the "engine" is
built, would consist in the exploration of NEW options:

1) "Deep" Physics Patterns

First and foremost, the tool can facilitate finding 
"hidden symmetries and NEW patterns", because it can be 
used to explore and abstract "rules within the rules"  
that would represent higher order "Physics Patterns" 
(hence the tool's name!).

Basically, with a tool that is capable of finding 
and testing symmetries it would be *EASY* to find 
new symmetries in complex Lagrangians -- this could 
in fact lead to the discovery of new conserved 
quantities (i.e. Noether's theorem).

In time, the goal is to connect these patterns, 
in autocatalytic chains, as described in:
http://www.livingmetaphor.org/pattern-languages-autocatalytic-
system.html
to understand the self-organizing life and dance 
of Nature.


2) Unified Theories

As higher order patterns would be found, the tool 
could also facilitate the exploration of ever more Unified 
theories because the effort of proposing NEW valid 
Unified Lagrangians and carrying all the calculations 
through the end would be greatly reduced.


3) Exploration of Quantum Computing

Because the tool accepts generalized propagators, 
quantum computing considerations can be built at 
*any* level of structure, for any interacting
particles, therefore the entanglement of *any
particles* i.e. gluons, photons, gravitons, etc. 
could be computed and explored.


4) Physics is Software

In light of the above patterns in 1) and Quantum Computing 
explorations in 3), the tool could help provide clues or 
explanations to support the worldview that 
"Physics is Software", that particles and energy are 
equivalent to "data/programs" transformed in a discrete
quantum space-time "memory/programs" depending on 
information-related rules.  One of the most interesting 
questions is "where is the program?" (I have postulated 
that they are in both in the evaluating space time 
(memory/evaluator/computer) and in the particle 
(data/program), suggesting a Lisp-like environment!!!): 
http://www.physicsissoftware.com


5) Variants in the end-to-end process

Because the tool would look at the process end-to-end, 
"configurable variants" of the tool could explore 
things like:

* looking beyond the "harmonic paradigm" -- universally 
accepted from QED, to LQG!, but harder to accept 
as the "only unique option" long term.
* new gauge fixes
* avoidance of unnecessary gauge fixes
* new formalisms not dependent on "exponentials of 
either Hamiltonians or Lagrangians", but other 
functional choices.
* exploration of strong couplings
* derivative powers of space-time > 2, still conforming
to Lorentz invariance or other gauge invariances
* discrete space-time (ala LQG or Matrix String Theory)
* non-commutative geometries


6) Exploration of Dual theories

The tool would make it easier to show that different 
theories are equivalent, both in the algebraic
and computational senses.  So things like String 
theory duality, LQG unifications, and comparisons 
with QED, electroweak, QCD, etc.; could be done 
or done faster.


7) Nonlinear Optics

(I had to include this one :-)

The tool can also help in the understanding of 
Non-Linear Optics, by studying the fundamental 
nonlinear scattering processes in greater detail.  
(Both Yariv's and Shen's books provide with QED-like 
analysis that could be further elaborated and 
explored -- an area I could never explore when 
I was a graduate student because of the complexity 
and hence time-requirements of the subject.)

8) Condensed Matter Physics and Collective Phenomena.

Since condensed matter physics and other collective 
phenomena also uses a great deal of similar 
computational techniques, the tool can also be 
used to explore this area with greater detail and 
complexity i.e. Chern-Simons, Quantum Hall fluids, 
superconductivity, topological field theory, 
superfluids, Hawking radiation, critical phenomena, 
phonons, solitons, vortices, monopoles, instantons, etc.


IV. APOLOGIA

I know all of the above is quite a mouthful, keep in mind
Rome was not created in one day but also that without a vision, 
we wouldn't had gone to the Moon :-)  ... So, yes, 
it is a long-term project.  Maybe longer than 
my lifetime :-)

I will really appreciate any feedback anyone may have!


- Mike Beedle
http://www.mikebeedle.com

"I am always doing things I can't do, that's how I get to do them."

    --Pablo Picasso