Amy Cuddy — American Psychologist

Amy Joy Casselberry Cuddy is an American social psychologist known for her research on stereotyping and discrimination, emotions, power, nonverbal behavior, and the effects of social stimuli on hormone levels. She is an Associate Professor of Business Administration at Harvard Business School, in the Negotiation, Organizations & Markets Unit. Her TED talk, delivered at TEDGlobal 2012 in Edinburgh, Scotland, and posted in October 2012, has been viewed more than 27 million times and ranks second among the most-viewed TED talks... (wikipedia)

Trust is the conduit for influence; it's the medium through which ideas travel.
Politicians are very experienced - maybe too experienced - at using body language to signal power and competence. But what these politicians are much more likely to struggle with, or just neglect to do altogether, is communicate warmth and trustworthiness.
I sometimes work with a communications and media training firm called KNP Communications. It's nice to bring the research to the practitioners; I learn a lot watching how they put it into practice, and I know they like to be on top of what's happening on the research front.
It's not uncommon for people to overvalue the importance of demonstrating their competence and power, often at the expense of demonstrating their warmth.
A lot of politicians, not surprisingly, hire consultants to help them with their nonverbals, presence, generally how they come across.