Firstly, your argument is flawed in that you assume that the study of physics (as a discipline) is THE definition of something being physical, and if something is not physical (i.e., not studied via physical sciences), it must be "mental". This is simply incorrect. Secondly, "solid proofs" only exist in mathematics - science can never "prove" much of anything, yet provides evidence that strengthens or weakens the likelihood of a particular theory being true. In fact, the entire faculty of science rests on the idea that nothing can ever be proven definitively; but evolutionary theory is one of the few theories that is as close as we can get to proof in science.

Remember, Darwinian evolution describes the origin of species, not the origin of life. It describes how living species change over time, not how they came to be. Although our understanding of how evolution works has changed since Darwin proposed his theory (for example, we now understand that it is populations that evolve, not individuals), many of the underlying concepts of Darwin's original idea remain true.

As stated by your colleague, evolution does not directly say anything about matter - nor should it. However, that does not mean it is an imaginary phenomenon that is simply "mental" in its scope. There are many direct observations of evolution in action, dating all the way back to 1901 with Huge de Vries and his observations of the Evening Primrose. More recent work by Dr. Richard Lenski using  Escherichia coli is another fantastic example of observing evolution in action (I suggest reading Dr. Richard Dawkins' book "The Greatest Show on Earth" for an exceptional display of the evidence for evolution, including direct observations).

Although Darwinian evolution in itself does not describe how life first originated (again, nor should it have to), there is evidence that provides some insight as to how life may have formed from a "primordial soup". Some fantastic work being done by Dr. Martin Hanczyc (http://flint.sdu.dk/index.php?page=martin-hanczyc) and colleagues suggests that life could very well have evolved from a complex mixture of chemicals under the right conditions. For simplicity, watch the TED Talk from Dr. Hanczyc below;  I've also included citations to a few of his peer-reviewed papers that will be of value to you. There is still much work to be done, but Dr. Hancyzc's work is starting to elucidate a mechanism(s) by which life may have originated from a mixture of chemicals. 

Hanczyc TED Talk: 1. http://www.ted.com/talks/martin_hanczyc_the_line_between_life_and_not_life?language=en

Hanczyc publications:

1. Hadorn M, et al. 2012. Specific and Reversible DNA-directed Self-Assembly of Oil-in-Water Emulsion Droplets. PNAS, doi: 10.1073/pnas.1214386109.

2. Horibe N, et al. 2011. Mode Switching and Collective Behavior in Chemical Oil Droplets. Entropy 13, 709-719; doi:10.3390/e13030709

3. Hanczyc MM, and Ikegami T. 2010. Emergence of Self-Movement as a Precursor to Darwinian Evolution. OLEB 40(4-5): 383. Conference abstract.

1) what physical the Physics is missing to study?

2) "nothing can ever be proven definitively." I argue. Take a physical system: White House. There can be president.

You are researcher. What to do? You go in there and see the President. You go out of system and write a paper: today, June 2014 the President was in White House. This is useful scientific result. It is the solid proof for the court, that the president can not kill child in China same time and date.

3) evolution, which ignores his borders is "mental case". A) In the beginning was the first cell. B) dead matter is not alive. Thus, you have nonsense in the beginning of evolution. Thus, all evolution is "mental case"

4) Me: you are not theist, so you are materialist. The love, the kindness, goodness, kissing child "good night" is all matter. All what you ever have experienced or ever be is matter. But "evolution does not... say anything about matter", so it is "mental case". I am theist and disagree.

1. Could you please clarify? I am confused as to the meaning of your statement.

2. You cannot definitively "prove" that the person you saw was the President. There will ALWAYS be some level of uncertainty as to the identity of someone (it may have been a look-alike, twin, etc.; even if you had DNA testing conducted, these tests are not absolutely 100% accurate).

3. Who is "he"? If you are referring to a God, then you are saying that anything that ignores God's (whichever God you are referring to) borders is mental and therefore not physical. This would be a self-fulfilling statement and is nonsensical. Also, the "nonsense" you refer to is not defined and seems to be ill-advised and an illegitimate term for your argument. Again, watch the TED Talks and read the publications from Dr. Hanczyc - these suggest that what you're referring to as nonsense and "dead matter" can indeed evolve into a functioning, living organism.

4. The examples of matter you give, like evolutionary theory, do not directly say anything about matter. For example, when you speak of love, you are not directly speaking of the properties of matter, but are speaking of an emotion of humans, whom themselves are made of matter (yet the prospect of "love" isn't made of matter, thought the processes that result in "love" may be). In that sense, evolution, "speaks" of matter indirectly (just as love, kindness, goodness, etc.), as it describes how living species evolve, and living species are made of matter. Therefore evolution must be physical and not "mental", as you define it.