Physics Derivation from Primary Literature

Proof required

Submit the full citation of the primary paper you have selected, a statement of the specific result or derivation within it that you will work through, and a high-level step map showing the key logical stages of the derivation (what physical assumptions are made, what mathematical technique is applied at each stage, and what the intermediate results are before the final result).

What gets checked

• The selected result is from an identifiable primary literature source — a published or preprint paper with authors, title, and journal or arXiv reference; not a textbook derivation
• The derivation is non-trivial — it requires more than three substantive steps and involves at least one technique above introductory-level physics (variational methods, perturbation theory, Green's functions, renormalisation group, tensor notation, or equivalent)
• The step map distinguishes physical assumptions from mathematical manipulations — the two are different and a physics derivation requires clarity about where each type of reasoning is applied

Common mistakes

• Selecting a result whose derivation appears in standard textbooks — the primary literature source must provide something beyond what is in textbooks; a standard derivation presented in a new paper does not add to the challenge
• Attempting the step map without reading the full paper — the derivation usually depends on notation and definitions established earlier in the paper; skipping the context creates errors in later steps

Resources

What a verifier looks for

• Ask the submitter to explain the physical motivation for the result before any algebra — confirms they understand why the derivation exists and what physical question it answers.
• Ask what assumptions the derivation rests on — physics derivations are only valid within their assumptions; understanding the boundaries of validity is essential.
• Ask the submitter to confirm the result reduces to a simpler known result in an appropriate limit — checking limiting cases is the standard self-verification in theoretical physics.

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Proof required

Submit your complete written derivation in LaTeX or equivalent mathematical notation. Every step must be numbered. Every non-trivial step must be annotated with its justification (naming the identity used, the approximation applied, or the physical assumption invoked). Any steps that the original paper skipped must be filled in. The derivation must end by confirming the result matches the paper's stated result.

What gets checked

• Every step is numbered and annotated — not a transcription of the paper but a re-derivation with explicit justification at each step
• Compressed or skipped steps in the original paper are expanded — confirming the paper's result requires showing the missing algebra, not assuming the authors were correct
• Approximations are identified with the conditions under which they are valid — an approximation that is not accompanied by its validity condition is unjustified in a physics derivation

Common mistakes

• Transcribing the paper's derivation rather than re-deriving it — copy-paste of equations is not a derivation; each step must be re-worked independently
• Assuming that steps that appear obvious are correct without checking — in physics derivations, 'obvious' steps are frequently where sign errors, factor of 2 errors, and dropped terms appear

Resources

What a verifier looks for

• Point to a specific step in the derivation and ask the submitter to explain it in physical terms, not mathematical terms — the physics behind each algebraic step is where genuine understanding is demonstrated.
• Ask the submitter to check one intermediate result against a limiting case — does the expression reduce to the correct simple result when a parameter is set to zero or infinity?
• Ask why a specific approximation was made at the step where it appears — what physical condition makes it valid and when would it break down?

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Proof required

Submit the final derivation document and a Q&A record showing: the specific step or claim the reviewer challenged, the submitter's real-time response to at least one novel modification the reviewer proposed (a changed parameter, a different limit, or a relaxed assumption), and the reviewer's assessment of whether the derivation is correct. The reviewer must be named and their physics background (research area, degree, or professional physics role) stated.

What gets checked

• Q&A record documents a genuine physics challenge — not confirmation of correctness but a specific modification or novel scenario the reviewer introduced
• Submitter's response to the novel modification demonstrates physical reasoning — not just 'the algebra would change' but an analysis of what physical effect would enter or which term would dominate in the modified case
• Final derivation incorporates any corrections identified during the review

Common mistakes

• A reviewer who only verifies correctness without posing modifications — the purpose of the oral examination is to test physical understanding, not endorse correctness; a reviewer who does not probe the submitter's reasoning is not fulfilling the examination role
• A reviewer without physics expertise in the relevant subfield — a mathematician can verify algebra but cannot assess whether the physical reasoning behind each step is correct

Resources

What a verifier looks for

• Introduce a modification — change one parameter from the derivation (a different coupling constant, a non-zero mass, a different boundary condition) and ask how the derivation would change.
• Ask the submitter to identify where in the derivation a specific physical effect enters — e.g., 'at what step does the choice of boundary condition affect the result?'
• Ask what the result implies about an observable — connecting the mathematical result to a physical measurement is the final test of whether the derivation is understood as physics rather than algebra.

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