#### The Basis of Physics:

The appended pages summarize what I think about
why physics exists. It just relies
on the existence of weakly interacting entities separable in space and time as
well as on the existence of hierarchies of vastly different energy scales.
If all of physics would happen more or less at the same energy scale, i.e. if
no hierarchies of different energy scales would exist, one would have to
understand all of physics at once. In other words, one would need to know the
"Theory of Everything" (TOE) in order to even get started.

#### Effective Field Theory:

Fortunately, in our world it is sufficient to identify the relevant degrees of
freedom at a given energy scale, to be aware of symmetries, and to respect
locality in space and time, in order to construct systematic Effective Field
Theories (EFT). In this way, by building a network of EFTs step by step in
scale, we patch together a quantitative description of the world from low to
high energy scales. For this, prior knowledge of the TOE is not necessary at
all. Here are some reviews about the EFT method by:
D. B. Kaplan,
A. Pich, and
R. Shankar.

#### Model Building:

It is often useful to build a model of some aspect of the world, by
again identifying the relevant degrees of freedom and respecting symmetries as
well as locality. Some experts consider the Hubbard model as the theory of
everything that is essential for high-temperature superconductivity. Similarly,
QCD, which is part of our most fundamental description of Nature, and thus
more than just a model, can be viewed as the "Theory of Everything" about the
strong interaction.

#### Numerical Simulations:

Since they serve as "Theories of Everything" about a certain class of
phenomena, models are often so complex that they still cannot be solved
analytically. In that case, numerical simulations may serve as a very powerful
tool. Here are two very useful websites with explanations and demonstrations:
by M. Creutz, as well as the
ALPS
project by M. Troyer and collaborators.

#### Graphical Tensor Product Reduction:

When describing physical systems with Lie algebras it is vital to reduce tensor
products of irreducible representations into sums of such representations.
The graphical tensor product reduction scheme of J. P. Antoine and D. Speiser
provides an algorithm to calculate these sums, without engaging in long and
tedious calculations. An implementation of this particular tensor product
reduction scheme for the Lie algebra so(5) can be found in
here. The su(3) implementation is
there.